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Prove that angle ABC is a isosceles triangle,if the altitude AD BISECTS THE BASE BC

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maths
Abc is a triangle where ad bisects angle a and d is the midpoint of bc prove that triangle is isosceles

Math
If the bisector of the vertical angle of the triangle bisects the base prove that the triangle is isosceles?

geometry
AD is an altitude of an isosceles triangle ABC in which AB=AC. Show that AD bisects BC.

Math
In a diagram of an 2 isosceles triangles, where ABC is a big triangle and a ADE, is just inside the top portion of ABC. Isosceles triangle ABC is similar to a isosceles triangle ADE what is the length of DE, which is the base part of a isosceles triangle ADE ? Do you just take...

Geometry
Can you help me with Always, Sometimes, Never questions?? I have answered all of these, but I am not sure if they are right. 1. The base angle of an isosceles triangle are acute----Always 2. When the altitude and the median are drawn from the same vertex of a triangle, the ...

Geometry Honors
Can someone help me with Always, Sometimes, Never questions?? I have answered all of these, but I am not sure if they are right. 1. The base angle of an isosceles triangle are acute----Always 2. When the altitude and the median are drawn from the same vertex of a triangle, the...

Maths
X and Y are points on the sides BC and AC of a triangle ABC respectively such that angle AXC = angle BYC and BX = XY. Prove that AX bisects the angle BAC. I believe the first step is to prove ABXY is a cyclic quadrilateral. Unfortunately, I don't know how!!!

Maths
ABC is an isosceles triangle in which the equal sides are AB and A.If AD is an altitude and |BC|=1/2|AB|.Prove that |AD|^2=15|BC|^2

geometry
prove in an isosceles triangle ABC,in which AB=AC and AD is the altitude,AD is also: i-median ii-bisector<A.

math
The base of triangle ABC is one half the altitude.The altitude of triangle DEF is one half its base. If both triangles are equal in area, what is the ratio of the altitude of triangle ABC to the altitude of triangle DEF ? a. 1:4 b. 1:2 c. 1:1 d. 2:1 e. 4:1 please answer and ...

math
The base of triangle ABC is one half the altitude. The altitude of triangle DEF is one half its base. If both triangles are equal in area, what is the ratio of the altitude of triangle ABC to the altitude of triangle DEF? a. 1:4 b. 1:2 c. 1:1 d. 2:1 e. 4:1 please answer and ...

Math(Geometry)
In the diagram below(no diagram but details will be provided), right triangle ABC and line BD is an altitude to side line AC. * Prove that (AB)^2=(AC)(AD) -When you label the triangle B should be were the right angle is C should be at the top of the triangle and it should be ...

Geometry
Given: segment BD bisects angle ABC; AB=BC. Prove: triangle ABD congruent to triangle CBD

math
In isosceles right triangle ABC, point D is on hypotenuse BC such that AD is an altitude of triangle ABC and DC = 5. What is the area of triangle ABC?

Geometry- how to write proof
ABC is a right triangle. Angle C is 90 degree. Altitude CD is drawn to hypotenuse AB. Prove AB/BC = BC/BD and AB/AC = AC/AD This is a theorem. How do I prove it? Thanks. Dont you have similar triangles? You can show this by looking at the angles involved...remember the ...

Euclidean Geometry
I am in the 10th Grade and my question is: The base of an isosceles triangle is 21cm. long. The altitude to the base is 9cm. long. What is the approx. measure of a base angle of the triangle? The tangent of that angle is 9/10.5 = 0.8571 Trigonometric tables will tell you that ...

geometry
TWO COLUMN TRIANGLE PROOF Given: line AB is parallel to line DE, and line AD bisects line BE Prove: triangle ABC is congruent to triangle DEC by using the ASA (angle-side-angle) postulate

geometry
if the isosceles triangle abc has one base angle of 2x-20 and the other base angle x+10 then what is the measure of angle b given the choices 36,40, 44, and 48

corollary to isosceles triangle theorem
how to prove 1)the measure of each angle of an equilateral triangle is 60. 2)the bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. Thanks. 1) The angles in any triangle have to add up to 180 degrees, right? 3 x 60 = 180 2) ?? 2. ...

SAT math
Can someone please double check my true and false answers! 1. All cylinders are prisms: TRUE 2. The angle opposite a side length of 6 cm in a triangle is larger than an angle opposite a side length of 7 cm in the same triangle: FALSE 3. The perpendicular bisector of the base ...

Geometry
1. In an isosceles triangle that is not equilateral the angle between the congruent sides is called a ____ A> Leg B> Vertex C> Base D> Corollary <<<<<<<<THIS ONE 2. In triangle ABC, AB = CB, m<ABC = 4x-3, and m<CAB = x-3. What is m<...

maths
in triangle abc angle b = 2angle c.d is a point ob bc such that ad bisects angle bac and ab = cd.prove that angle bac = 72

Isoceles Angle Bisector
Triangle ABC is isosceles with AB=AC. D is a point on BC such that AD bisects ∠BAC. What is the measure of ∠ADB (in degrees)?

Geometry
Given:-AD is perpendicular to BC -Triangle ABC is isosceles with vertex angle A Prove: Triangle ADB congruent to Triangle ADC (note: it should be solved in 9 steps and I got 7 steps and it being SAS)

Geometry
Do the altitudes of an isosceles triangle go to the midpoints of the opposite sides? My triangle ABC is isosceles with points A (0,0), B (a,b), and C (2a,0). My diagram shows that the altitude from A will hit side BC at point N and the altitude from C will hit side AB at point...

Geometry
In triangle ABC, AD bisects angle A, BD=4 and CD=5. The perimeter of triangle ABC is 29. Find the lengths of AB and AC.

geometry
Prove that the angle bisectors of the base of the isosceles angles of the isosceles triangle are congruent using statement and reason proof i dont really now how to prove this problem but i now what a transversal is and the angles of a trashes line. can u guys plz solve and ...

Geometry
Please answer at least one . PLEASE 1. Triangle XYZ has a right angle at Y. V,W are on XZ such that XV=XY. WZ=YZ, find ANGLE VYW . 2. STUVWXYZ is a regular octagon. Find SW/ TZ. 3. The interior angles of a convex polygon form an arithmetic progression with a common difference ...

math
a rectangle with side of 6 cm and 5 cm has the same area as an isosceles triangle with base length 12 cm find the altitude to the base of the triangle and the sides of the triangle

12th grade
Find altitude of isosceles triangle if angle=53 degrees and base is 8 inches.

trig
Find the altitude of an isosceles triangle whose base in 30 cm vertex angle is 75 degres

geometry
the base of an isosceles triangle is 18 centimeters long. The altitude to the base is 12 centimeters long. What is the approximate measure of a base angle of the triangle?

geometry proofs
given ABC is a triangle. Ad is the altitude to BC. Ad biscects angle BAC. Prove: Ad is the median to BC

Geometry
Let ABC be any triangle. Equilateral triangles BCX, ACY, and BAZ are constructed such that none of these triangles overlaps triangle ABC. a) Draw a triangle ABC and then sketch the remainder of the figure. It will help if (triangle) ABC is not isosceles (or equilateral). b) ...

geometry
how do you find the height of an isosceles triangle only knowing the lengths of all three bases? EX: There's isosceles triangle ABC with vertex angle B. AB= 5x-28. BC= 2x+11. AC= x+5

geometry
the vertices of triangle ABC are A(1,7)B(9,3)C(3,1) a.prove that the triangle is a right triangle b.which angle is the right angle? c.which side is the hypotnuse? d.what are the coordinatesof the midpoint of the hypotnuse? e.what is the equation of the median from the vertex ...

trig
Find altitude of isosceles triangle if angle=53 degrees (the equal angles) and the base is 8 inches.

Geometry
The altitude to the hypotenuse of a right triangle ABC divides the hypotenuse into 12mm and 16mm segments. Find the lengths of each of the following. A. The altitude to the hypotenuse B. The shorter leg of angle ABC C. The longer leg of angle ABC

geometry
Each base of an isosceles triangle measures 42 degrees, 30'. The base is 14.6 meters long. a. Find the length of a leg of the triangle b. Find the altitude of the triangle c. What is the area of the triangle?

GEOMETRY
GIVEN: TRIANGLE ABC,AD bisects <BAC,and AE=ED, PROVE:AE/AC=BD/BC

Geometry - semicircle inside isosceles triangle
Isosceles triangle ABC has sides of length AB=AC=25 and BC=40 . Find the area of a semicircle inscribed in triangle ABC with diameter along BC . Please help I do not know how to start....

Geometry
The perimeter of triangle ABC is 29 meters. Line segment AD bisects angle A. Find AB and AC. CD=5cm, DB=4 cm.(triangle angle bisector theorem)

mathematics
in triangle abc if acosA= bcosB then how to prove the triangle is isosceles or right angled

Math
In triangle ABC, D bisects side BC, G bisects side AB, and the points E and F trisect side AC. What is the area of the shaded polygon, if the area of ABC is 108? I tryed to find the area of triangles on the side and I figured that if you put a line from the top of the triangle...

Math
In triangle ABC, D bisects side BC, G bisects side AB, and the points E and F trisect side AC. What is the area of the shaded polygon, if the area of ABC is 108? I tryed to find the area of triangles on the side and I figured that if you put a line from the top of the triangle...

Math please help urgent
In triangle ABC, D bisects side BC, G bisects side AB, and the points E and F trisect side AC. What is the area of the shaded polygon, if the area of ABC is 108? I tryed to find the area of triangles on the side and I figured that if you put a line from the top of the triangle...

wgu qlc
isosceles proof prove that angle dgf is isoceles given line eg bisects angle def edg is congruent to efg

Math-CHECK PLEASE
Which of the statements is ALWAYS TRUE? A-A right triangle is a scalene triangle. B-An equilateral triangle is an isosceles triangle. C-An isosceles triangle is an obtuse triangle. D-A right triangle is an acute triangle. I got either A or D. I don't know. Also, if angle A is ...

9th grade
given that a(-1,8) ,b(2,4) and if the line y=4 is the axis of symmetry of triangle abc find c.show that triangle abc is an isosceles triangle,calculate the area of triangle abc,calculate the perpendicular distance from a to bc

Trigonometry
Each base angle of an isosceles triangle measures 42°. The base is 14.6 feet long. A) Find the length of a leg of the triangle. Round to the nearest tenth of a foot. B) Find the altitude of the triangle. Round to the nearest tenth of a foot.

Trigonometry
Each base angle of an isosceles triangle measures 42°. The base is 14.6 feet long. A) Find the length of a leg of the triangle. Round to the nearest tenth of a foot.  B) Find the altitude of the triangle. Round to the nearest tenth of a foot.

math
ABC is an isosceles triangle. AB=BC=6. Angle ABC=120,AC=a square root of b. What is a+b?

math
an altitude of triangle is 5/3rd of the length of its corresponding base if their altitude be increased by 4cm and the base is decreased by 2cm, the area of the triangles remain the same. find the base and altitude of triangle ?????

Math
Triangle ABC is an isosceles triangle with angle A= 40 degrees. Give three possible values for angle B

geometry
I have right triangles I need to solve. Can you see if I am doing them correctly or screwed up..1) Rt < is in left corner C: Opposite is 60 deg< A, last angle is at top- 30 deg <. line segment of AB is 10. Hypo is f. I got 10 0r 12.5 for answer. 2) Triangle is ABC ...

geometry
Points D, E, and F are the midpoints of sides \overline{BC}, \overline{CA}, and \overline{AB} of \triangle ABC, respectively, and \overline{CZ} is an altitude of the triangle. If \angle BAC = 71^\circ, \angle ABC = 39^\circ, and \angle BCA = 70^\circ, then what is \angle EZD+\...

geometry
Points D, E, and F are the midpoints of sides \overline{BC}, \overline{CA}, and \overline{AB} of \triangle ABC, respectively, and \overline{CZ} is an altitude of the triangle. If \angle BAC = 71^\circ, \angle ABC = 39^\circ, and \angle BCA = 70^\circ, then what is \angle EZD+\...

Geometry
Points D, E, and F are the midpoints of sides \overline{BC}, \overline{CA}, and \overline{AB} of \triangle ABC, respectively, and \overline{CZ} is an altitude of the triangle. If \angle BAC = 71^\circ, \angle ABC = 39^\circ, and \angle BCA = 70^\circ, then what is \angle EZD+\...

geometry
Triangle ABC is an isosceles triangle, where angle B is the vertex angle. If BC = 10x-4 , AC= 2x+18 , and AB= 6x+32, find the value of x.

math
in an isosceles triangle ABC ,AB=AC.if AB and AC are produced to D and E respectively so that BD=CE.prove thatBE=CD

math
in an isosceles triangle ABC ,AB=AC.if AB and AC are produced to D and E respectively so that BD=CE.prove thatBE=CD

help math
In triangle ABC, points D,E,F are on sides BC,CA,AB respectively such that AD,BE,CF are angle bisectors of triangle ABC. The linesAD,BE,CF are concurrent at I,the incenter of triangle ABC. If Angle BAC=90, what is the measure (in degrees) of Angle EIF?

geometry
how long are the congruent legs of isosceles triangle if its base and altitude to the base are 12cm and 8 cm respectively?

geometry
how long are the congruent legs of isosceles triangle if its base and altitude to the base are 12cm and 8 cm respectively?

geometry
how long are the congruent legs of isosceles triangle if its base and altitude to the base are 12cm and 8 cm respectively?

Math
The base of an isosceles triangle is 4x cm long.The altitude to the base is 6cm long.Find the length of a leg of the triangle.

math
ABC is a isosceles triangle. Line B extended to D. Prove that <ACD = 90 degree.

Geometry
Equilateral triangle ABC and isosceles triangle DBC share side BC. If angle BDC= 34 and BD=BC, what is the measure of angle ABD? I don't know how to solve this questions, can someone guide me through?

geometry
Equilateral triangle ABC and isosceles triangle DBC share side BC. If angle BDC= 34 and BD=BC, what is the measure of angle ABD? I don't know how to solve this questions, can someone guide me through?

math
Triangle $ABC$ is a right triangle with right angle at $A$. Suppose $\overline{AX}$ is an altitude of the triangle, $\overline{AY}$ is an angle bisector of the triangle, and $\overline{AZ}$ is a median of the triangle, and $\angle XAY = 13^\circ$. If $X$ is on $\overline{BY...

geometry
In isosceles triangle ABC, AB = BC, and D is a point between A and C on AC. Can you conclude MO > ML, MN > MO, angle L > angle BDA, or angle N > angle BDC

MATHS
the base BC of a triangle ABC is divided at D so that BD=1/3 BC .prove that ar(triangle ABD)=1/2 ar (triangle ADC)

Geometry
1. The perimeter of an isosceles triangle is 50cm and the length of the altitude to the base is 5cm. Find the length of the base. 2. In quadrilateral QRST: TQ=8cm; (angle)R=60; (angle)T=90; QR=RS; ST=8cm. Find the exact length of the longer diagonal of the quadrilateral.

Math (Geometry)
The perimeter of right triangle ABC is equal to the perimeter of isosceles triangle DEF. The lengths of the legs of the right triangle are 6 and 8. If the length of each side of the isosceles triangle is an integer, what is the greatest possible length for one of the sides of ...

geometry
I need to figure out this proof, the figure is two triangles forming a rhombus. Given: segment BD is the angle bisector of triangle ABC and triangle ADC Prove: Triangle ABD is congruent to Triangle CBD So far I have segment BD is the angle bisector of triangle ABC and triangle...

Math- any help would be greatly appreciated
In triangle ABC, the medians AD,BE, and CF concur at the centroid G. (a) Prove that AD < (AB + AC)/2. (b) Let P=AB+AC+BC be the perimeter of triangle ABC. Prove that 3P/4 < AD + BE + CF < P.

Geometry
in triangle ABC, BD bisects <ABC, <ABD = 4x + 6 and m<DBC = 5x -5. find the m<abc

Math
In an isosceles triangle, the perimeter is 8 more than 2 times on of the legs. If the perimeter is 28 in, find the length of the base. A. 16 in B. 18 in C. 10 in D. 8 in Given triangle ABC with A(-3, 2), B(-1, -4), and C(4, 1), write the equation for the line containing ...

math
Triangle LNK is isosceles and line LK is the base. use a paragraph proof to prove that triangle LNK is equal to triangle KNM

math
show that abc is a right angled isosceles triangle prove that AD>AC and AC>CD also arrange in ascending order

math
in the triangle ABC , AD ray bisects the exterior angle of the triangle at A and intersects CB ray at D . if AB = 6 cm , AC = 8 cm , and BC = 5 cm , find the length of BD line segment

math
The base (BC) of an isosceles triangle (ABC) is also the side of a square (BCEF) in which the triangle is inscribed. A perpendicular line is drawn in the triangle from B to AC at D, forming triangle ABD. What is the ratio of triangle ABD to the square BCEF?

geometry
I sent question about rt triangle, ABC, needing to find a & b. altitude was 4, base a and hypotenuse b. You mentioned knowing another angle. There is one < A is 45 degrees. Thanks for all your help. Math is not an easy subject for me.

geometry
The medial triangle of a triangle ABC is the triangle whose vertices are located at the midpoints of the sides AB, AC, and BC of triangle ABC. From an arbitrary point O that is not a vertex of triangle ABC, you may take it as a given fact that the location of the centroid of ...

geometry
In a triangle ABC,E and F are the mid-points of AC and AB respectively. The altitude AP to BC intersects EF at Q.Prove AQ =PB.

Geometry HELP
An isosceles triangle ΔABC has its altitude at the y-axis and its base at the x-axis. D is the midpoint of segment AC and E is the midpoint of segment CB. Given the coordinates A(-2a, 0), B(2a, 0), and C(0, 2b), determine the coordinates of midpoints D and E. a.)D(2a,-b); ...

Geometry Help
1.) An isosceles triangle ΔABC has its altitude at the y-axis and its base at the x-axis. D is the midpoint of segment AC and E is the midpoint of segment CB. Given the coordinates A(-2a, 0), B(2a, 0), and C(0, 2b), determine the coordinates of midpoints D and E. a.)D(2a,-...

Math
Let A (2, 3); B (-2, -1) and C (5, -2) be vertices of triangle ABC. If the line connected by points B and C is the base of these triangle and the line bisected through point A is the altitude then what will be the area of the triangle?

Maths (quadratic equation) need help
The altitude of a triangle is 3 less than twice its base.The area of the triangle is 10m^2. Find the altitude and base of the triangle.

maths
In an isosceles triangle angle in the top vertex is twice the sum of the base angle. Find the exterior angles of the triangle.

Algebra
Triangles ABC and DEF are similar. Find the area of triangle ABC. Round your answer to the nearest tenth. Triangle ABC has a base of 12m. Triangle DEF has a base of 18m and height of 12m

Agent HELP! Trigonometry
An isosceles triangle ABC has two sides 17cm in length and a base 10cm in length. Find the size of the angle between the equal sides.

Math
The two sides of a isosceles triangle have a fixed lenght of 14 cm. The opposite angle at the base of the triangle increases by 0.3 rad/min. a) what is the growth rate dx/dt of the base of the triangle when the opposite angle mesures 1.6 rad? (Use the law of sin) b) What is ...

Math
The two sides of a isosceles triangle have a fixed lenght of 14 cm. The opposite angle at the base of the triangle increases by 0.3 rad/min. a) what is the growth rate dx/dt of the base of the triangle when the opposite angle mesures 1.6 rad? (Use the law of sin) b) What is ...

Math
The two sides of a isosceles triangle have a fixed lenght of 14 cm. The opposite angle at the base of the triangle increases by 0.3 rad/min. a) what is the growth rate dx/dt of the base of the triangle when the opposite angle mesures 1.6 rad? (Use the law of sin) b) What is ...

Math
The two sides of a isosceles triangle have a fixed lenght of 14 cm. The opposite angle at the base of the triangle increases by 0.3 rad/min. a) what is the growth rate dx/dt of the base of the triangle when the opposite angle mesures 1.6 rad? (Use the law of sin) b) What is ...

maths
In triangle ABC angle B > angle C if AM is the bisector of angle BAC and AN perpendicular BC. prove that angle MAN =1/2(angle B - angle C)

Math
If the ratio of a base angle and vertical angle of an isosceles triangle is 1:2 find the angles of the triangle

Math
In triangle ABC, the medians AD,BE, and CF concur at the centroid G. (a) Prove that AD < (AB + AC)/2. (b) Let P=AB+AC+BC be the perimeter of triangle ABC. Prove that 3P/4 < AD + BE + CF < P.

Geometry
Given triangle ABC, AD bisects angle BAC,and AE=ED Prove AE/AC=BD/BC Because I cant draw it I will explain. Its a triangle, A is the point at the top, B is the point at the bottom left and C is the point at the bottom right.There is a line going right down the middle, which is...

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