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Chapter 4: Q4. (page 132)

Decide whether the two triangles must be congruent. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

Short Answer

Expert verified

No congruence can be deduced

Step by step solution

01

Step 1. First observation from figure.

Line segments AC¯and BD¯are congruent

So,AC¯≅BD¯

02

Step 2. Second observation from figure.

Line segments CF¯and DF¯are congruent

So,CF¯≅DF¯

03

Step 3. Third observation from figure.

∠AFCand∠DFB are vertically opposite angles and thus congruent

So,∠AFC≅∠DFB

04

Step 4. Conclude given two triangles are congruent or not.

From step 1, 2, and 3

Two sides and one angle is congruent

But it does not satisfies any postulate

Thus, congruency cannot be deduced

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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 ΔABC. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

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.

State whether the congruence of triangles have the reflexive property, the symmetric property, the transitive property.

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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