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Chapter 4: Q10. (page 160)

Write proofs in two-column form.

Given: ∠JMK≅∠LMK; MK¯⊥plane P.

Prove: JK¯≅LK¯

Short Answer

Expert verified

The proof in two-column form is:

Step by step solution

01

- Observe the given diagram.

The given diagram is:

02

- Description of step.

It is being given that∠JMK≅∠LMK and MK¯⊥plane P.

In the triangles ▵MKJand ▵MKL, the side that is common is MK.

Therefore, MK¯≅MK¯by using the reflexive property.

As, MK¯⊥plane P, therefore m∠MKJ=90° and m∠MKL=90°.

Therefore, ∠MKJ≅∠MKL.

In the triangles ▵MKJand ▵MKL, it can be noticed that ∠JMK≅∠LMK, MK¯≅MK¯ and∠MKJ≅∠MKL.

Therefore, the triangles ▵MKJ and ▵MKL are the congruent triangles by using the ASA postulate.

The triangles ▵MKJ and ▵MKL are the congruent triangles.

Therefore, by using the corresponding parts of congruent triangles it can be said that JK¯≅LK¯.

03

- Write the conclusion.

The proof in two-column form is:

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Most popular questions from this chapter

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