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Chapter 4: Q21. (page 138)

Given:OP炉鈮�OQ炉;鈭�3鈮�鈭�4

Prove:鈭�5鈮�鈭�6

Short Answer

Expert verified

It is proved that 鈭�5鈮�鈭�6.

Step by step solution

01

Step 1. Vertically opposite angles.

From the figure it can be observed that,鈭�POS and鈭�QOR are vertically opposite angles. Therefore, 鈭�POS鈮�鈭�QOR.

02

Step 2. ASA postulate.

If two angles and included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Here, 鈭�3鈮�鈭�4,OP炉鈮�OQ炉 and 鈭�POS鈮�鈭�QOR, then by ASA postulate width="112" height="20" role="math">螖POS鈮�螖QOR.

03

Step 3. Description of step.

As螖POS鈮�螖QOR, implies that sides of congruent angles are congruent, that is, OS炉鈮�OR炉.

04

Step 4. Isosceles triangle theorem.

If two sides of triangle are congruent then the angles opposite to those sides are congruent.

Consider螖OSR,as OS炉鈮�OR炉, therefore, by isosceles triangle theorem, 鈭�5鈮�鈭�6.

Hence it is proved that, 鈭�5鈮�鈭�6.

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Most popular questions from this chapter

Draw a right triangle. Then draw its three altitudes in color.
  1. Name the coordinates of points A, B, and C.
  2. Name the coordinates of a point D such that螖ABC鈮�螖ABD.

A town wants to build a beach house on the lakefront equidistant from the recreation center and the school. Copy the diagram and show point B where the beach house should be located.

b. The town also wants to build a boat-launching site that is equidistant from Elm Road and Main Street. Find the point L where it should be built.

c. On your diagram, locate the spot Ffor a flagpole that is to be the same distance from the recreation center, the school, and the courthouse.

Is the following statement 鈥淐orresponding parts of congruent triangles are congruent鈥� based on a definition, postulate, or theorem?

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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