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Chapter 4: Q1 (page 121)

Write proof in two-column form.

Given: AD炉鈯�BC炉; BA炉鈯�AC炉.

Prove: 鈭�1鈮�鈭�2.

Short Answer

Expert verified

The two-column proof is:

Statements

Reasons

1. AD炉鈯�BC炉; BA炉鈯�AC炉

1. Given

2. 鈭�BACand 鈭�BDAare right angles.

2. Definition of鈯�lines.

3. 螖BACand 螖BDAare right triangles.

3. Definition of right triangles.

4. 鈭�1and 鈭�Bare complementary angles; 鈭�2and 鈭�Bare complementary angles.

4. The acute angles of a right triangle are complementary.

5.鈭�1鈮�鈭�2

5. If two angles are complementary of the same angle, then the two angles are congruent.

Step by step solution

01

Step 1. Consider the diagram.

Here,AD炉鈯�BC炉;BA炉鈯�AC炉

02

Step 2. State the proof.

The two triangles are said to be congruent if they are copies of each other and if their vertices are superposed, then say that the corresponding angles and the sides of the triangles are congruent.

The two-column proof is:

Statements

Reasons

1.AD炉鈯�BC炉;BA炉鈯�AC炉

1. Given

2. 鈭�BACand鈭�BDA are right angles.

2. Definition of鈯�lines.

3. 螖BACand 螖BDAare right triangles.

3. Definition of right triangles.

4. 鈭�1and 鈭�Bare complementary angles; 鈭�2and 鈭�Bare complementary angles.

4. The acute angles of a right triangle are complementary.

5.鈭�1鈮�鈭�2

5. If two angles are complementary of the same angle, then the two angles are congruent.

03

Step 3. State the conclusion.

Therefore, 鈭�1鈮�鈭�2( proved).

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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.

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to 螖ABCIf 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?

For the following figure, does the SAS postulates justify that the two triangles are congruent.

For the following figure, can the triangle be proved congruent. If so, what postulate can be used?
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