Question

chapter 2 continued
name hugo cruz
date
chapter test a
for use after chapter 2
find the measure of a complement and supplement of the angle.
11.
12.
in exercises 13 and 14, find m∠1, m∠2, and m∠3.
13.
14.
in exercises 15 and 16, underline the hypothesis and circle the conclusion of the if - then statement.

1. if it rains, then you will need an umbrella.
2. if an angle is a straight angle, then its measure is 180°.

in exercises 17 and 18, what can you conclude from the given true statements?

1. if two angles form a linear pair, then they are supplementary. two angles form a linear pair.

conclusion:

1. if the basketball player makes the shot, then we win the game. the basketball player makes the shot.

conclusion:
write the statement that follows from the pair of true statements.

1. if the perimeter of a square is 24 inches, then the length of a side is 6 inches.

if the length of a side of a square is 6 inches, then the area of the square is 36 square inches.
use the property to complete the statement.

1. reflexive property of equality: m∠d =?
2. transitive property of congruence: if (overline{pq}congoverline{rs}) and (overline{rs}congoverline{tu}), then?(cong)?

Explanation:

Step1: Recall complement - angle formula

Complementary angles add up to 90°. For a 11° angle, the complement is 90° - 11°.
$90 - 11=79$

Step2: Recall supplement - angle formula

Supplementary angles add up to 180°. For a 11° angle, the supplement is 180° - 11°.
$180 - 11 = 169$

Step3: Recall vertical - angle property for 13

Vertical angles are equal. In the figure for 13, ∠1 and the 50° angle are vertical angles, so $m\angle1=50$. ∠2 and the 50° angle are also vertical angles, so $m\angle2 = 50$. ∠3 and ∠1 are supplementary (linear - pair), so $m\angle3=180 - 50=130$.

Step4: Recall vertical - angle and linear - pair properties for 14

∠1 and the 115° angle are supplementary (linear - pair), so $m\angle1=180 - 115 = 65$. ∠2 and the 115° angle are vertical angles, so $m\angle2 = 115$. ∠3 and ∠1 are vertical angles, so $m\angle3=65$.

Step5: Identify hypothesis and conclusion for 15

The hypothesis is "it rains" and the conclusion is "you will need an umbrella".

Step6: Identify hypothesis and conclusion for 16

The hypothesis is "an angle is a straight angle" and the conclusion is "its measure is 180°".

Step7: Draw conclusion for 17

Since "if two angles form a linear pair, then they are supplementary" and "two angles form a linear pair", the conclusion is "the two angles are supplementary".

Step8: Draw conclusion for 18

Since "if the basketball player makes the shot, then we win the game" and "the basketball player makes the shot", the conclusion is "we win the game".

Step9: Combine statements for 19

If the perimeter of a square is 24 inches, then the length of a side is 6 inches, and if the length of a side of a square is 6 inches, then the area of the square is 36 square inches. So, if the perimeter of a square is 24 inches, then the area of the square is 36 square inches.

Step10: Apply reflexive property for 20

By the reflexive property of equality, $m\angle D=m\angle D$.

Step11: Apply transitive property for 21

If $\overline{PQ}\cong\overline{RS}$ and $\overline{RS}\cong\overline{TU}$, then $\overline{PQ}\cong\overline{TU}$ by the transitive property of congruence.

Answer:

1. Complement: 79°, Supplement: 169°
2. Complement: 90 - 57=33°, Supplement: 180 - 57 = 123°
3. $m\angle1 = 50$, $m\angle2 = 50$, $m\angle3=130$
4. $m\angle1 = 65$, $m\angle2 = 115$, $m\angle3=65$
5. Hypothesis: it rains; Conclusion: you will need an umbrella
6. Hypothesis: an angle is a straight angle; Conclusion: its measure is 180°
7. The two angles are supplementary
8. We win the game
9. If the perimeter of a square is 24 inches, then the area of the square is 36 square inches
10. $m\angle D$
11. $\overline{PQ}\cong\overline{TU}$