# 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?

### 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- 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 ...

### 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

### 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

in triaangle ABC, AB=20 cm, AC=15 cm the length of the altitude AN is 12 cm prove that ABC is a right triangle so far i got that angle ANC is 90 degrees by definition on altitude i got really confused after so can you show me how to answer the question and the soulotion please.

### 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

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

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

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

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

### trig

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

### 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 ...

### 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...

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

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 ...

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 ?????

### 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 ...

### Math

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

### 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

### 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?

### 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?

### 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 (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

If lines AB=6cm, AC=10cm, BC=2•4cm, CD=4cm and AD=X cm. Also angle ABC = angle ACD. (a).Prove that triangle ABC is similar to triangle ACD. (b).Determine the area of the quadrilateral ABCD if the area of triangle ACD is 60cm^2

### 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.

### 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 ...

### Geometry

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

### 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

### 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.

### 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?

### 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

### Geometry HELP

An isosceles triangle Î”ABC 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 Î”ABC 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,-...

### 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

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 ...

### 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.

### Maths

The vertical angle of an isosceles triangle is twice the sum of the base angles. Find each angle of the triangle??

### 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 ...

### 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.