geometry
posted by DEE
in triangle ABC, PandQ are points on BC such that BQ=CP and AP=AQ.show thatAB=AC

Arora
In this case, APQ forms an isoceles triangle, which you'll see if you draw a figure. (AP=AQ)
So, ∠APQ = ∠AQP
=> 180  ∠APQ = 180  ∠AQP
=> ∠AQB = ∠APC .....1
Now, consider triangles AQB and APC
AP = AQ (Given in the question)
∠AQB = ∠APC (From ...1)
QB = PC (Given in the question)
Hence, the two triangles AQB and APC are congruent by the SAS rule.
Since the corresponding parts of congruent triangles are equal, AB=AC
Respond to this Question
Similar Questions

geometry
Triangle ABC is a 45°45°90° triangle inscribed in a sphere such that B is the center of the sphere, and A and C are points on the sphere. Given the hypotenuse of ABC is 32 units, what is the surface area of the sphere? 
geometry
Triangle ABC is a right triangle such that m angle B= 90 degrees. If AC= 12 and BC=9, what is the perimeter of triangle ABC ? 
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 lines AD,BE,CF are concurrent at I, the incenter of triangle ABC. If ∠BAC=92∘, what is the measure … 
heeeeeeeeeeeeeeeeeeeelp maths
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 lines AD,BE,CF are concurrent at I, the incenter of triangle ABC. If ∠BAC=92∘, what is the measure … 
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 … 
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) … 
Math
In Triangle ABC, medians BE and CD are produced respectively to points X and Y such that CD=DX and BE=EY as shown in the figure. Show that the points X, A and Y are collinear. Also show that A is the mid point of XY 
maths
In TRIANGLE ABC points P,Q,R arethe points lies inside triangle in such a way that Ap= PR, BQ=QP &QR=RC n area of triangle PQR =100 then find the Area of ABC 
maths
In TRIANGLE ABC points P,Q,R arethe points lies inside triangle in such a way that Ap= PR, BQ=QP &QR=RC n area of triangle PQR =100 then find the Area of ABC 
MATH
In Triangle ABC, medians BE and CD are produced respectively to points X and Y such that CD=DX and BE=EY as shown in the figure. Show that the points X, A and Y are collinear. Also show that A is the mid point of XY