Question

look at the figure. name the postulate or the theorem you can use to prove the triangles congruent

A. ASA Postulate
B. SAD Postulate
C. SSS Postulate
D. AAS Postulate

Answer 1

Answer:

A. ASA

Step-by-step explanation:

ASA is a postulate that states that if two triangles have two angles and one side congruent, the side being the included side, then the angles are congruent.

Answer 2

The two triangles are congruent and it can be proved using ASA postulate. The correct option is A.

What are congruent triangles?

Suppose it is given that two triangles ΔABC ≅ ΔDEF

Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.

The order in which the congruency is written matters.

For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.

Thus, we get:

$\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF$

(|AB| denotes length of line segment AB, and so on for others).

For the two triangles to be congruent we can write the following condition,

In ΔWTU and ΔUVW,

WU ≅ WU {The common side of the two triangles}

∠TUW ≅ ∠VUW {Given}

∠TWU ≅ ∠VWU {Given}

Since the measure of the two angles in two triangles is the same, also, the length of the side between the two angles will be equal for both the triangles.

Therefore, the two triangles are congruent and it can be proved using ASA postulate.

Learn more about Congruent triangles:

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