Benchmark II Review

Point T is at (-6,-8) and point M is at (14,12). What is the slope of segment TM?

• -1

• 1

• -10

• 20

Tags

CCSS.8.EE.B.5

 Given:    p: a bee has a stinger    

                q:  bee can sting

What would be the symbolic representation for:

If a bee can sting, then a bee has a stinger.

• ~p --> ~q

• q --> p

• p --> q

• ~q --> ~p

Answer explanation

replace bee sting with q

and stinger with p

Given s // t and n//m.

What angle is congruent to angle 1?

• angle 10

• angle 13

• angle 16

• angle 15

Answer explanation

Remember use your angles

alternate interiors are congruent

alternate exteriors are congruent

consecutive interior are supplementary

consecutive exterior supplementary

corresponding are congruent

Or find the pattern and determine which are equal

Check out the image to help you determine which are congruent to angle 1.

Tags

CCSS.8.G.A.5

Transversal n passes through line s, q, v, p, and a.

Which lines are parallel?

Choose all that apply.

• s//p

• v//q

• s//a

• a//q

• a//v

Answer explanation

Remember, the angles created by a transversal and parallel lines are alternate interior/exterior, consecutive interior/exterior, or corresponding. So they are either congruent or supplementary. Look for congruent angles or angles with a sum of 180.

105+75=180 (consecutive interior)

and

102+78=180 (consecutive exterior)

Vertical angles are = so you you know those are congruent (refer to image)

Therefore s//p and a//q because consecutive angles = 180.

Tags

CCSS.8.G.A.5

Triangle DEF ~ Triangle GHI with a scale factor of 1 to 5. The sides of triangle DEF are 2 cm, 3 cm, and 6 cm.

• 10 cm, 15 cm, 24 cm

• 15 cm, 20 cm, 10 cm

• 15 cm, 30 cm, 10 cm

• 12 cm, 15, cm 10 cm

Answer explanation

Similar triangles have proportional sides. If the ratio is 1:5.

Multiply each side by 5 to find the new sides

2x5=10

3x5=15

6x5=30

If the ratio was 1:6, you would multiply each side by 6. Use this strategy to for missing sides of a similar triangle.

Tags

CCSS.7.G.A.1

What value of x would make the triangles congruent?

• 2

• 1

• 4

• -2

Answer explanation

4 + 2x = -6 ( x - 2)

plug in desmos to find answer

Remember SAS prove triangles are congruent so that means all side are equal to corresponding sides.

Tags

CCSS.HSG.CO.B.7

A segment as an endpoint of (9,-3) and a midpoint of (-8,-4). Where is the other endpoint located?

• (1/2, -3.5)

• (-25,-5)

• (1/2, 3.5)

• (26,-2)

Answer explanation

Remember add both endpoints and divide by 2 to get the midpoint.

To find the endpoint add the given endpoint to the missing endpoint, divide by 2 and set it equal to the given midpoint.

(9+x)/2=-8

(-3+y)/2=-4

Plug in Desmos and solve for the missing x and y

Tags

CCSS.HSG.GPE.B.6

List the angles in order from least to greatest.

• angle D, angle E, angle G

• angle D, angle G, angle E

• angle E, angle D, angle G

• angle G, angle E, angle D

Answer explanation

Remember the smallest angle is across from the shortest side.

order sides from shortest to longest

13.2 side DG

14.7 side GE

15.8 side DE

If side DG is the shortest then the smallest angle is E and the longest side is DE so the largest angle is G.

Tags

CCSS.HSG.CO.C.10

If a number is divisible by 9, then the number is odd.

What is a counterexample to the following?

• 27

• 45

• 18

• 63

Answer explanation

remember the first part stays true and the second is false

so a number divisible by 9 that is not odd but even

Given line m // line n, solve for x.

• 32

• 28

• 57

• 53

Answer explanation

The given angles are consecutive exteriors, so they are supplementary.

use -2x+5+4x+61=180

Plug in desmos to solve for x.

Tags

CCSS.8.G.A.5