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Chapter 4: Q7 (page 124)

For the following figure, can the triangle be proved congruent. If so, what postulate can be used?

Short Answer

Expert verified

The triangles are congruent by the SAS postulate.

Step by step solution

01

Step 1. Apply the concept of the SAS postulate.

SAS postulates state that if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.

02

Step 2. Check the figure.

Consider the figure.

03

Step 3. Step description.

From the figure, two sides of one triangle are congruent to two sides of another triangle also the included angles between two sides are equal as they are vertically opposite angles.

So, they must be equal.

Therefore, the triangles are congruent by SAS postulates.

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Most popular questions from this chapter

Plot the given points on graph paper. Draw ΔABCand ΔDEF. Copy and complete the statement ΔABC≅?¯.

A−7,−3B−2,−3C−2,0

D0,1E5,1F0,−2

Explain how you would prove the following. Given that HY¯≅LY¯,WH¯||LF¯. Prove that ΔWHY≅ΔFLY.

Draw and label a diagram. List, in terms of the diagram, what is given and what is to be proved. Then write a two-column proof.

In an isosceles triangle, if a segment is drawn from the vertex of the angle between the congruent sides to the midpoint of the opposite side, then congruent triangles are formed.

In the following figure, the two-triangle shown are congruent. Then complete the following statement.

ΔABO≅Δ___

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to ΔABC. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.
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