Question

There are two claims made about the right triangles below. Use the sketches at the right of each claimto help you explain what makes the triangles similar

Answer 1

Note:

For two or more triangles to be similar, they must be equiangular, that is , they must have equal angles

For question a, all we are intersested in proving is that triangles ABC, ACD and CBD have equal angles

In triangles ABC, In triangles ABC and ACD, they both have common angle A which are equal

Since two angles of triangles ABC and ACD are equal, then their third angle too must be equal ( i.e < B = < C)

In triangles ABC and CBD, they both have coomon angle B,

Therefore, their third angles are equal

hence, since we have established that the 3 triangles are equiangular, therefore they are similaar triangles

Part B

In triangles CAB, line FG joins the midpoint of AC and CB, therefore line FG is parallel to line AB (the line joining the midpoints of two side of a triangle is parallel to the third side)

therefore,

in triangle CFG, in triangle CFG, in triangle CGFSince we have established that triangle CFG and triangle CAB have equal angles, they are similar triangles