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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

For the following figure, do the SAS postulates justify that the two triangles are congruent?

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

___鈮�螖CTA

Draw and label a diagram. List, in terms of the diagram, what is given and what is to be proved. Then write a two-column proof.

In an isosceles triangle, if the angle between the congruent sides is bisected, then two congruent triangles are formed.

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

For the following figure, (a) List two pairs of congruent corresponding sides and one pair of congruent corresponding angles in 螖YTRand 螖XTR. (b) Notice that, in each triangle, you listed two sides and nonincluded angle. Do you think that SSA is enough to guarantee that two triangles are congruent?
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