Question

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

Answer 1

Answer:

Therefore,

ΔABD ~ ΔACB by Angle-Angle Similarity Postulate

AB is 8 unit.

Step-by-step 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.  

$\dfrac{AB}{AC} =\dfrac{AD}{AB} \textrm{corresponding sides of similar triangles are in proportion}$  

Substituting the values we get

$\dfrac{AB}{16} =\dfrac{4}{AB}\\\\(AB)^{2}=64\\AB=\sqrt{64}=8\ unit$

Therefore,

ΔABD ~ ΔACB by Angle-Angle Similarity Postulate

AB is 8 unit.