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Chapter 4: Q19 (page 126)

Write proofs in two-column form.

Given: PlaneM bisects AB炉;PA炉鈮�PB炉

Prove:鈻�POA鈮�鈻�POB

Short Answer

Expert verified

The two-column proof is:

Statements

Reasons

MbisectsAB炉

Given

AO炉鈮�BO炉

Definition of midpoint

PA炉鈮�PB炉

Given

PO炉鈮�PO炉

Reflexive property

鈻�POA鈮�鈻�POB

SSS postulate

Step by step solution

01

Step 1. Observe the figure.

The figure is:

02

Step 2. Description of step.

Given thatplaneMbisects AB炉 and PA鈮�PB.

Therefore, by using the definition of midpoint, it can be said that AO=OB.

That implies, AO鈮�OB.

In the triangles 鈻�POA and 鈻�POB, it can be noticed that PO=PO by using the reflexive property.

That implies, PO鈮�PO.

Therefore, it can be seen that AO=OB,PO=PO and PA=PB.

Therefore, the triangles 鈻�POA and 鈻�POB are congruent triangles by using the SSS postulate.

03

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

The proof in two-column form is:

Statements

Reasons

MbisectsAB炉

Given

AO炉鈮�BO炉

Definition of midpoint

PA炉鈮�PB炉

Given

PO炉鈮�PO炉

Reflexive property

鈻�POA鈮�鈻�POB

SSS postulate

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Most popular questions from this chapter

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.

Plot the given points on graph paper. Draw 螖ABCand 螖DEF. Copy and complete the statement 螖ABC鈮�?炉.

A鈭�1,2B4,2C2,4

D5,鈭�1E7,1F10,鈭�1

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 you are given a scalene triangle and a point Pon some line localid="1648799479069" l. How many triangles are there with one vertex at localid="1648799462577" P, another vertex on localid="1648799472074" l, and each triangle congruent to the given triangle?

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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