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Chapter 4: Q10. WE (page 137)

For each exercise place the statements in an appropriate order for a proof. (There may be more than one correct order.)

Given: BD¯||CE¯;∠5≅∠6

Prove:AC¯≅AE¯

(a)BD¯||CE¯

(b)AC¯≅AE¯

(c) ∠5≅∠C;∠6≅∠E

(d)∠5≅∠6

(e) ∠C≅∠E

Short Answer

Expert verified

Order of the proof is a,d,c,eandb.

Step by step solution

01

Step 1. Apply the definition of corresponding angles.

From the given figure it can be observed that ∠5and∠Cand ∠6and∠Dare corresponding angles and therefore they are equal, that is,

∠5≅∠C∠6≅∠E

02

Step 2. Transitive property of congruence.

If∠P≅∠Q and∠Q≅∠S then ∠P≅∠S.

Since,∠5≅∠6 and∠5≅∠C;∠6≅∠E implies that ∠C≅∠E.

03

Step 3. Converse of isosceles triangle theorem.

If two angles of a triangle are congruent, then the sides opposite to those angles are congruent.

From the given figure it can be observed that AC¯is opposite to ∠Eand AE¯is opposite to ∠C.

As ∠C≅∠E,AC¯≅AE¯

From the above explanation, the order of proof is a,d,c,eandb.

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Most popular questions from this chapter

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