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If it is given that AB¯¯¯¯¯¯¯¯≅CB¯¯¯¯¯¯¯¯, how can it be proved that m∠A=m∠C?

If it is given that AB¯¯¯¯¯¯¯¯≅CB¯¯¯¯¯¯¯¯, how can it be proved that m∠A=m∠C?-example-1
User Neilon
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1 Answer

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Given:

Line AB ≅ Line CB

Let's prove that m∠A ≅ m∠C.

Given that side AB is congruent to side CB, to prove that the measure of angle A is congruent to the measure of angle C, we have:

The first step is to draw an angle bisector from B to a point D such that point D is on AC.

The next step is to show that the corresponding sides and the angle between the sides of the new triangles ABD and CBD are congruent.

Since triangle ABD and triangle CBD are congruent, we are to use the Side-Angle-Side Congreunce postulate and the definition of congruent angles to show that measure of angle A is congruent to the measure of angle C.

ANSWER:

Draw an angle bisector from B to a point D such that point D is on AC. Then show that corresponding sides and the angle between the sides of the new triangles ABD and CBD are congruent. Finally, use the Side-Angle-Side postulate and the definitio

User Manav Mehra
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