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Chapter 4: Q11. (page 151)

Given that BC¯≅CD¯,BD¯≅CE¯then prove thatΔABCis isosceles.

Short Answer

Expert verified

ΔABCis isosceles.

Step by step solution

01

Step 1. Check the diagram.

Consider the diagram.

02

Step 2. Apply the concept of SSS postulate.

SSS Postulate states that

If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

03

Step 3. Step description.

Consider the triangles: ΔBECandΔCDB

BE¯≅CD¯

BD¯≅CE¯⇒EC¯≅DB¯

BC¯≅CB¯

Thus, by SSS Postulate, ΔBEC≅ΔCDB.

So, ∠EBC≅∠DCB⇒∠B≅∠C.

Therefore,ΔABC is isosceles

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Most popular questions from this chapter

For the following figure, does the SAS postulates justify that the two triangles are congruent.

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.

Suppose that ΔBIG≅ΔCAT, then complete the following statement.

BI=__

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.

Name the coordinates of a point G such that Is there another location for G such that

ART
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