Question

Cut out To Identical Right Angle Triangles Name The Vertices Of The Trangel As A B C On North Side Drew The Altitude On The Hyvotenuse Of One Of Them Name The Foot Of The Perpendicular As D Cut The Trangel On Tya Altitude And Obtain Two Trangels State The Correspondences By Wich Three Trangels Are Similar With One Another ​

Answer 1

Given :  Right angle triangle ABC

To Find :  Similar triangles

Solution:

ΔABC

∠B = 90°

∠A + ∠C  = 90°

=> ∠A = 90° - ∠C

and  ∠C = 90° - ∠A

AD  ⊥ BC

ΔADB

∠ADB = 90°

∠A

∠ABD = 90° - ∠A = ∠C

AD  ⊥ BC

ΔCDB

∠CDB = 90°

∠C

∠CBD = 90° - ∠C = ∠A

ΔADB  and ΔBDC

∠ADB = ∠CDB  = 90°

∠A  = ∠CBD

∠ABD = ∠C

AAA  similarity

ΔADB  and ΔABC

∠ADB = ∠B  = 90°

∠A  =  ∠A

∠ABD = ∠C

AAA  similarity

ΔCDB  and ΔCBA

∠CDB = ∠B  = 90°

∠C  =  ∠C

∠CBD = ∠A

AAA  similarity

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