Triangle Similarity Proof: Comparing Triangles ABD and ADC with Heights of 7 and 15 Units

Question

Are triangles ΔABD and ΔADC similar?

00:00 Are the triangles similar?

00:03 The triangle is isosceles according to the given data

00:08 In an isosceles triangle, the height is also a median (T)

00:15 Legs are equal in an isosceles triangle (T)

00:23 Common side between the triangles (T)

00:29 The triangles are congruent by SAS

00:35 Congruent triangles are necessarily similar

00:38 And this is the solution to the question

Since side AB is equal to side AC, the triangle is isosceles.

AD divides BC into two equal parts, therefore BD = DC.

Also, AD is a common side.

From this, it follows that the triangles are similar according to the S.S.S (side side side) criterion.

Yes, according to S.S.S.