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Chapter 4: Q.15 (page 161)

Write proofs in two-column form.

Given: GH炉鈯�HJ炉; KJ炉鈯�HJ炉; 鈭�G鈮�鈭�K

Prove:鈻�GHJ鈮�鈻�KJH

Short Answer

Expert verified

The proof in two-column form is:

Step by step solution

01

Step 1.  Observe the given diagram.

The given diagram is:

02

Step 2.  Description of step

It is being given that GH炉鈯�HJ炉,KJ炉鈯�HJ炉and 鈭�G鈮�鈭�K.

As, GH炉鈯�HJ炉, therefore by using the definition of perpendicular lines it can be said that m鈭�GHJ=90掳.

As, KJ炉鈯�HJ炉,therefore by using the definition of perpendicular lines it can be said that m鈭�KJH=90掳.

Therefore, m鈭�GHJ=m鈭�KJH=90掳.

Therefore, 鈭�GHJ鈮�鈭�KJH.

In the triangles 鈻�GHJ and 鈻�KJH, it can be noticed that the side HJ is common.

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

In the triangles 鈻�GHJ and 鈻�KJH, it can be noticed that 鈭�G鈮�鈭�K, 鈭�GHJ鈮�鈭�KJH and HJ炉鈮�HJ炉.

Therefore, the triangles 鈻�GHJ and 鈻�KJH are congruent triangles by AAS postulate.

03

Step 3.  Write the proof in two-column form.

The proof in two-column form is:

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Most popular questions from this chapter

OR炉is a common side of two congruent quadrilaterals.

Complete: quad.NERO鈮�quad?炉.

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to 螖ABC. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

Suppose that 螖BIG鈮�螖CAT, then complete the following statement.

鈭�G鈮�__

Copy each three-dimensional figure and with coloured pencils outline the triangles listed. What postulate proves that these triangles are congruent?

Given: Cube whose faces are congruent squares.

Show: 鈻�ABF,鈻�BCG

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to 螖ABC. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.
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