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Chapter 4: Q.14 (page 161)

Complete.

If ∠1≅∠2, ES=3y+5, ET=25-y, then y=?¯.

Short Answer

Expert verified

The value ofy is 5.

Step by step solution

01

Step 1.  Observe the given diagram.

The given diagram is:

02

Step 2.  Write the theorem 4-2.

The theorem 4-2 states that if two angles of a triangle are congruent, then the sides opposite to those angles are congruent.

03

Step 3.  Description of step

As, ∠1=∠2, therefore the sides opposite to the angles ∠1 and ∠2 are also equal.

Therefore, it can be noticed that ES¯≅ET¯.

04

Step 4.  Find the value of y.

ES¯=ET¯3y+5=25−y3y+y=25−54y=20y=204y=5

Therefore, the value of y is 5.

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Most popular questions from this chapter

Given:ΔABC in plane M; D not in plane M;

∠ACB≅∠ABC;∠DCB≅∠DBC

Name a pair of congruent triangles. Prove that your answer is correct.

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to ΔABCIf 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 complete the following statement.

AO¯≅___

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.

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.

25. If pentagonABCDEv is equilateral and has right angles at Band E, then diagonals AC¯and AD¯form congruent triangles.
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