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Chapter 4: Q4. (page 142)

For the following figure, state which congruence method can be used to prove the triangle congruent. If no method applies, say none.

Short Answer

Expert verified

The triangles are congruent by the SASpostulate.

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, in both the triangles one pair of right angles and two pairs of equal angles.

Using the Isosceles triangle theorem, sides opposite to equal angles are also equal.

So, there are two pairs of equal sides.

Therefore, the triangles are congruent by SASpostulates.

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Most popular questions from this chapter

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

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

Deduce that DC炉鈭�AB炉.

Suppose that 螖BIG鈮�螖CAT, then complete the following statement.

___鈮�螖CTA

For the following figure, do the SAS postulates justify that the two triangles are congruent?

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.

If a line perpendicular to AB炉passes through the midpoint of AB炉, and segments are drawn from any other point on that line to and , then two congruent triangles are formed.
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