Question

Given AB/CD = AO/OC = BO/OD Prove: <1 is congruent to < 2

Answer 1

The common ratio of the corresponding sides of the given triangles

indicate that the triangles are similar.

• ∠1 is congruent to ∠2 by CASTC

Reasons:

The given relationship are;

• $\displaystyle \frac{AB}{CD} =\frac{AO}{OC} = \mathbf{\frac{BO}{OD}}$

The ratio of each side of ΔAOB to the corresponding side of ΔCOD is constant, therefore;

ΔAOB is similar to ΔCOD by Side-Side-Side similarity postulate

Which gives;

ΔAOB ~ ΔCOD

Therefore, the three angles of ΔAOB are congruent to their corresponding angles of ΔCOD, which gives;

• ∠1 ≅ ∠2 by CASTC

(CASTC); Corresponding Angles of Similar Triangles are Congruent

Learn more about triangle similarity postulates here:

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