Question

Identify two similar triangles in the figure, and explain why they are similar. Then find AB.

Answer 1

Therefore,

ΔABD ~ ΔACB by Angle-Angle Similarity Postulate

AB is 8 unit.

Explanation:

Given:

∠ABD ≅ ∠BCD

AD = 4

DC = 12 Therefore AC =AD + DC = 4 +12 =16

AC =16

To Find:

Similar Triangles

AB =?

Solution:

In ΔABD and ΔACB

∠ABD ≅ ∠ACB ……….{Given}

∠ A ≅ ∠ A .……..{Reflexive Property}

ΔABD ~ ΔACB ….{By Angle-Angle Similarity Postulate}

If two triangles are similar then their sides are in proportion.

`(AB)/(AC) =(AD)/(AB) \textrm{corresponding sides of similar triangles are in proportion}\\`

Substituting the values we get

`(AB)/(16) =(4)/(AB)\\\\(AB)^(2)=64\\AB=√(64)=8\ unit`

Therefore,

ΔABD ~ ΔACB by Angle-Angle Similarity Postulate

AB is 8 unit.