Unit 6/7 Test Review

Segment & Angle Addition (6-1)

100

If AB = 5 and BC = 7, what is AC?

AC=5+7=12

200

If ∠ABC=50^∘ and ∠CBD=40^∘, what is ∠ABD?

angle(ABD) = 50^@ + 40^@ = 90^@

300

Given that AB+BC=AC, solve for x if AB=2x+3, BC=x+5, and AC=16.

x=8/3

400

The measure of ∠XYZ is 4x+10 and ∠WYZ is 2x+20. If ∠XYZ+∠WYZ=90^∘, find x.

x=10

500

M is the midpoint of AB. If AM=3x−2 and MB=2x+6, find AB.

AB=28

Midpoint, Distance, & Pythagorean Theorem (6-3)

100

What is the formula for the midpoint of two points (x₁, y₁) and (x₂, y₂)?

("Midpoint Formula:") ((x_1 + x_2)/2, (y_1 + y_2)/2)

 

200

What is the distance between (2,3) and (6,7)?

d = sqrt((6-2)^2 + (7-3)^2) = sqrt(16 + 16) = sqrt(32) = 4sqrt(2)

300

A triangle has legs of 6 and 8. What is the hypotenuse?

c = sqrt(6^2 + 8^2) = sqrt(36 + 64) = sqrt(100) = 10

400

The midpoint of A(3, 7) and B(x, 9) is (5, 8). Find x.

(3 + x)/2 = 5 => 3 + x = 10 => x = 7

500

A right triangle has legs of 5x and 12x, and its hypotenuse is 13x. Find x.

(5x)^2 + (12x)^2 = (13x)^2 => 25x^2 + 144x^2 = 169x^2

, so x can be any real number.

Angle Relationships (6-7)

100

What is the sum of complementary angles?

90^∘

200

If two angles are supplementary and one is 60^∘, what is the other?

180^∘−60^∘=120^∘

300

Two vertical angles are represented as (3x+10)^∘ and (5x−20)^∘. Find x.

3x + 10 = 5x - 20 => x = 15

 

400

Angle A and Angle B are complementary. If Angle A is twice the measure of Angle B, find both angles.

A + B = 90^@ and A = 2B => 2B + B = 90 => B = 30^@, A = 60^@

 

500

If ∠1=(x+20)^∘ and ∠2=(2x−10)^∘, and they are vertical angles, find x.

x + 20 = 2x - 10 => x = 30

Parallel Lines & Transversals (7-1)

100

Name a pair of corresponding angles. *See Board*

Any pair of angle in the same relative position

200

Alternate interior angles are always ____.

Congruent

300

If a transversal creates one angle of 70^∘, what is the corresponding angle?

70^∘ (corresponding angles are equal)

400

Two parallel lines are cut by a transversal. If one alternate exterior angle is 110^∘, what is the other?

110^∘

500

Solve for x if a corresponding angle is (2x+10)^∘ and another is (4x−20)^∘.

2x + 10 = 4x - 20 => x = 15

 

Triangle Angle Theorems (7-3)

100

The sum of interior angles in a triangle is ___.

180^∘

200

What is the exterior angle theorem?

The exterior angle is equal to the sum of the two remote interior angles.

300

Find the missing angle: 40^∘, 60^∘, and ___.

180 - (40 + 60) = 80^@

400

If an exterior angle is 120^∘ and one interior angle is 50^∘, find the other interior angle.

120 = x + 50 => x = 70^@

500

Find x if the angles of a triangle are (2x+10)^∘, (3x−20)^∘, and (x+30)^∘.

(2x + 10) + (3x - 20) + (x + 30) = 180 => 6x + 20 = 180 => x = 40