Question

units 2 & 3 usa test review

1. if m∠xyz = 90°, find all of the following angle measures.

m∠1 = 55°
m∠2 = 35°
m∠3 = 55°
m∠4 = 35°
m∠5 = 55°

1. write the following statement as a conditional (\if - then\) statement.

conditional statement p→q
\two angles that have the same measure are congruent.\
a. if two angles are congruent, then they have the same measure.
b. if two angles have the same measure, then they are congruent.
c. if two angles are not congruent, then they do not have the same measure.
d. if two angles do not have the same measure, then they are not congruent.

1. identify the converse, inverse and contrapositive of the conditional statement...

\if the dolphins score a touchdown, they get six points.\
converse q→p inverse ¬p→¬q contrapositive ¬q→¬p
if the dolphins get six points, they scored a touchdown. a
if the dolphins dont get six points, they didnt score a touchdown. d
if the dolphins dont score a touchdown, they dont get six points. g

1. which value of x makes likes h and k parallel?

alternate interior angles
3(2x + 5)°=(2x + 18 - x)°
6x+15=x + 18
6x - x=18 - 15
5x = 3
x = 3/5
a. 1
b. 3/5
c. 3/7
d. 11

Explanation:

Step1: Identify angle - related properties

For question 1, use the fact that vertical angles are equal and complementary angles add up to 90°. For question 2, recall the form of a conditional statement. For question 3, use the definitions of converse, inverse and contra - positive. For question 4, use the property of alternate interior angles being equal for parallel lines.

Step2: Solve question 1

Since vertical angles are equal, if one of the non - right angles adjacent to the right angle ∠XYZ is 35°, then its vertical angle has the same measure. And the other non - right angle adjacent to the right angle is 90°−35° = 55°, and its vertical angle also has the measure of 55°.

Step3: Solve question 2

The given statement “Two angles that have the same measure are congruent” can be written as “If two angles have the same measure, then they are congruent”. So the answer is b.

Step4: Solve question 3

The converse of “If p then q” is “If q then p”, the inverse is “If not p then not q” and the contra - positive is “If not q then not p”. For “If the Dolphins score a touchdown, they get six points” (p: Dolphins score a touchdown, q: they get six points):

• Converse: “If the Dolphins get six points, they scored a touchdown” (A)
• Inverse: “If the Dolphins don't score a touchdown, they don't get six points” (H)
• Contra - positive: “If the Dolphins don't get six points, they didn't score a touchdown” (F)

Step5: Solve question 4

If lines h and k are parallel, then the alternate interior angles are equal. So 3(2x + 5)=(2x + 18−x).

• Expand the left - hand side: 6x+15.
• Simplify the right - hand side: x + 18.
• Then 6x+15=x + 18.
• Subtract x from both sides: 6x−x+15=x−x + 18, 5x+15 = 18.
• Subtract 15 from both sides: 5x+15−15=18−15, 5x = 3.
• Divide both sides by 5: x=\frac{3}{5}.

Answer:

1. m∠1 = 55°, m∠2 = 35°, m∠3 = 55°, m∠4 = 35°, m∠5 = 55°
2. b. If two angles have the same measure, then they are congruent.
3. Converse: A; Inverse: H; Contra - positive: F
4. b. \frac{3}{5}