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Chapter 4: Q20WE. (page 157)

Given: 鈻�LMN鈮�鈻�RST;LX炉and RY炉are altitudes.

Prove:LX炉鈮�RY炉

Short Answer

Expert verified

By corresponding parts of congruent triangles, it can be said thatLX炉鈮�RY炉.

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 鈻�LMN鈮�鈻�RST.

Therefore, LM鈮�RS, 鈭�LMN鈮�鈭�RST.

From the diagram, it can be seen that:鈭�LMN+鈭�LMX=180掳

and 鈭�RST+鈭�RSY=180掳.

Therefore, it can be obtained that:

鈭�LMN+鈭�LMX=鈭�RST+鈭�RSY鈭�LMN+鈭�LMX=鈭�LMN+鈭�RSY鈭�LMX=鈭�RSY

Therefore, 鈭�LMX鈮�鈭�RSY.

03

Step 3. Description of step.

From the given diagram it can be noticed that 鈭�LXM=鈭�RYS=90掳.

In the triangles 鈻�LMXand 鈻�RSY, it can be noticed that 鈭�LMX鈮�鈭�RSY, 鈭�LXM鈮�鈭�RYSand 鈻�RSY.

Therefore, the triangles 鈻�LMXand鈻�RSY are congruent triangles by using the AAS postulate.

Therefore, by corresponding parts of congruent triangles it can be said that LX炉鈮�RY炉.

Hence proved.

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Most popular questions from this chapter

Suppose that 螖FIN鈮�螖WEBname the three pairs of corresponding sides.

Complete.

A point lies on the bisector of an angle if and only if it is equidistant from .

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.

State whether the congruence of triangles have the reflexive property, the symmetric property, the transitive property.

Supply the missing statements and reasons.

Given: 鈭�Wand 鈭�Yare right angles; WX炉鈮�YX炉

Prove:WZ炉鈮�YZ炉
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