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Chapter 4: Q10. (page 160)

Write proofs in two-column form.

Given: 鈭�JMK鈮�鈭�LMK; MK炉鈯�plane P.

Prove: JK炉鈮�LK炉

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鈭�JMK鈮�鈭�LMK and MK炉鈯�plane P.

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

Therefore, MK炉鈮�MK炉by using the reflexive property.

As, MK炉鈯�plane P, therefore m鈭�MKJ=90掳 and m鈭�MKL=90掳.

Therefore, 鈭�MKJ鈮�鈭�MKL.

In the triangles 鈻�MKJand 鈻�MKL, it can be noticed that 鈭�JMK鈮�鈭�LMK, MK炉鈮�MK炉 and鈭�MKJ鈮�鈭�MKL.

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

The triangles 鈻�MKJ and 鈻�MKL are the congruent triangles.

Therefore, by using the corresponding parts of congruent triangles it can be said that JK炉鈮�LK炉.

03

- Write the conclusion.

The proof in two-column form is:

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