Free Printable Topic Test 5 & 6 Review Part 2

1.

Which is true about any midsegment in a triangle?

(Select all that apply.) #1

a)

The midsegment is parallel to its corresponding side.

b)

The midsegment is perpendicular to its corresponding side.

c)

The midsegment is half as long as its corresponding side.

d)

The midsegment connects the midpoints of two sides of a triangle.

e)

The midsegment is twice as long as its corresponding side.

2.

Match the following. #2

a)

Draw BD parallel to AC.

1.

Parallel Postulate

b)

m∠4+m∠2+m∠5=180∘

2.

Angle Addition Postulate and definition of straight edge

c)

∠1≅∠4, ∠3≅∠5

3.

Alternate Interior Angles Theorem

d)

m∠1=m∠4, m∠3=m∠5

4.

Definition of congruent angles

e)

m∠1+m∠2+m∠3=180∘

5.

Triangle Sum Theorem

3.

Reorder the steps for constructing a circumcenter of a triangle. #3

a)

Draw the perpendicular bisectors of all the sides of the triangle using a compass.

b)

Extend all the perpendicular bisectors to meet at a point. Mark the intersection point as O, this is the circumcenter.

c)

Using a compass and keeping O as the center and any vertex of the triangle as a point on the circumference, draw a circle, this circle is our circumcircle whose center is O.

1)

2)

3)

4.

Reorder the following steps for constructing an incenter of a triangle. #4

a)

Bisect one of the angles.

b)

Bisect another angle.

c)

Where they cross is the center of the inscribed circle, called the incenter.

d)

Construct a perpendicular from the center point to one side of the triangle.

e)

Place compass on the center point, adjust its length to where the perpendicular crosses the triangle, and draw your inscribed circle!

1)

2)

3)

4)

5)

5.

If $\angle ZXY\cong\angle ZYX$ and $\angle X=5t-13$ and $\angle Y=3t+3$ , what is $m\angle Z$ ? The figure is not drawn to scale. #5

(a)

6.

If $\angle LNM\cong\angle LMN$ and $\angle N=2x$ and $\angle M=x+30$ , what is $m\angle L$ ? The figure is not drawn to scale. #6

(a)

7.

Which theorem can we use to prove the two triangles are congruent? #7

a)

SSS

b)

SAS

c)

ASA

d)

AAS

8.

Are these triangles congruent? If so, state the rule which you used to determine congruence. #8

a)

SAS

b)

SSS

c)

Both SSS and SAS

d)

Not necessarily congruent

9.

Which triangles are congruent to A? #9

HINT: FIND THE THIRD ANGLE.

a)

b)

c)

d)

none of them

10.

$\Delta ABC\cong\Delta EDC$ Find the value of x that makes the two triangles congruent. #10

a)

11

b)

19

c)

38

d)

58

11.

Select all the congruent triangles. #11

a)

b)

c)

d)

12.

Select the congruent triangles. #12

a)

b)

c)

d)

13.

Which rule explains why these triangles are congruent? #13

a)

SAS

b)

ASA

c)

AAS

d)

SSS

14.

Which of the following does not represent the lengths of the sides of a triangle? #14

a)

2 cm, 6 cm, 7 cm

b)

5 cm, 2 cm, 5 cm

c)

5 cm, 5 cm, 8 cm

d)

3 cm, 10 cm, 15 cm

15.

What is the range of values of x for a triangle's third side given side measures of 8 and 15? #15

a)

between 8 and 15

b)

between 7 and 23

c)

less than 7, greater than 23

16.

Two sides of a triangle have the following measures. Find the range of possible measures for the third side. #16 $10,7$

a)

$5<x<16$

b)

$4<x<14$

c)

$4<x<17$

d)

$3<x<17$

17.

Two sides of a triangle have the following measures. Find the range of possible measures for the third side. $8,12$ #17

a)

$4<x<16$

b)

$5<x<20$

c)

$4<x<17$

d)

$4<x<20$

18.

Complete with >, < or =. #18

a)

>

b)

<

c)

=

d)

I don't know.

19.

Answer the question that follows. #19

a)

Plane 1

b)

Train 2

c)

Plane 2

d)

Train 1

20.

Compare the measure of angle Y and the measure of angle M. #20

a)

measure of angle Y = measure of angle M

b)

measure of angle Y > measure of angle M

c)

measure of angle Y < measure of angle M

d)

Not enough information is given.

21.

Choose the TRUE statement. #21

a)

$KL>MN$

b)

$KL<MN$

c)

$KL=MN$

d)

The above statements are all false.

22.

Compare QT and ST. #22

a)

$QT\ <\ ST$

b)

$QT\ >\ ST$

c)

$QT\ =\ ST$

d)

$\overline{QT}\ \cong\ \overline{ST}$

23.

Nigel and Mia are searching for a treasure chest underwater. The straight line distance between them is 100 meters. Given the angles in the diagram, who is closer to the treasure chest and why? #23

a)

Nigel is closer because his distance to the chest is opposite the larger angle.

b)

Mia is closer because her distance to the chest is opposite the smaller angle.

c)

Nigel is closer because his distance from the chest is 100 meters.

d)

Mia is closer because her distance from the chest is 100 meters.

24.

Triangle ABC is graphed on the set of axes below. What are the coordinates of the point of intersection of the medians of 𝛥𝐴𝐵𝐶? #24

a)

(-1,2)

b)

(-3,2)

c)

(0,2)

d)

(1,2)

25.

Which statement is always true given BC is the midsegment of triangle ADE? Select all that apply. #25

a)

$2AB=AD$

b)

$\overline{AD}\perp\ \overline{DE}$

c)

$\overline{AC}=\overline{CE}$

d)

$\overline{BC}\parallel\overline{DE}$

26.

What type of triangle is formed by the points A(4, 2), B(6,−1), and C(−1 3)? #26

a)

right

b)

equilateral

c)

isosceles

d)

scalene

27.

In this diagram, 𝐶𝐷 is the perpendicular bisector of 𝐴𝐵. The two-column proof shows that 𝐴𝐶 is congruent to 𝐵𝐶. Which of the following is the missing reason? #27

a)

AAS

b)

ASA

c)

SAS

d)

SSS

28.

In this figure, 𝒍||𝒎. Jessie listed the first two steps in a proof that ∠𝟏𝟏 + ∠𝟐𝟐 + ∠𝟑𝟑 = 𝟏𝟖𝟎°. Which justification can Jessie give for Steps 1 and 2? #28

a)

Alternate interior angles are congruent.

b)

Corresponding angles are congruent.

c)

Vertical angles are congruent.

d)

Alternate exterior angles are congruent

29.

One side of triangle XYZ has a length of 17 cm. Which pairs of lengths CANNOT be the lengths of the other two sides of the triangle? #29

a)

1 cm, 17 cm

b)

35 cm, 19 cm

c)

25 cm, 5 cm

d)

10 cm, 10 cm

30.

What construction is shown in the diagram? #30

a)

finding the perpendicular bisectors of the three sides of a triangle

b)

finding the bisectors of the three angles of a triangle

c)

finding the medians to the three sides of a triangle

d)

finding the altitudes to the three sides of a triangle

31.

What is true about △ABC? Select three options. #31

a)

$\overline{AB\ }\perp\ \overline{AC}$

b)

The triangle is a right triangle.

c)

The triangle is an isosceles triangle.

d)

The triangle is an equilateral triangle.

e)

$\overline{BC}\ \parallel\ \overline{AC}$

32.

Find the equation of the median, from vertex A to the opposite side, $\overline{BC}.$

A(9, 5), B(2, 5), C(4, 1) #32

a)

$y=\frac{3}{2}x+2$

b)

$y=\frac{5}{2}x+3$

c)

$y=2x+2$

d)

$y=\frac{1}{3}x+2$

33.

The coordinates of the vertices of RST are R(−2,−3), S(8,2), and T(4,5). Which type of triangle is RST? #33

a)

right

b)

acute

c)

obtuse

d)

equiangular

34.

Triangle ABC has vertices A(0,0), B(3,2), and C(0,4). The triangle may be classified as #34

a)

equilateral

b)

isosceles

c)

right

d)

scalene

35.

If the vertices of ABC are A(−2,4), B(−2,8), and C(−5,6), then ABC is classified as #35

a)

right

b)

scalene

c)

isosceles

d)

equilateral

36.

What are the coordinates of the centroid of

△JKL?

(x, y) ( (a) , (b) ) #36

Choose from the below words

2

4

0

5.5

1

5

4.5

37.

What are the coordinates of the centroid of △PQR?

(x, y) ( (a) , (b) ) #37

Choose from the below words

-5

5

-6.5

6

-3

5.5

38.

What are the coordinates of the centroid of △STU?

(x, y) ( (a) , (b) ) #38

Choose from the below words

-3

-1

-7.5

0

-1.5

39.

Mr. Gosser is practicing using his compass. What did he construct in this image? #39

a)

3 angle bisectors

b)

3 perpendicular bisectors

c)

A triangle

d)

3 circles

40.

The figure shows a circle circumscribed around a triangle. What is constructed first when creating the circle? #40

a)

perpendicular segments to the vertices of the triangle

b)

perpendicular bisectors of the sides of the triangle

c)

angle bisectors of each angle of the triangle

d)

the incenter of the triangle

Topic Test 5 & 6 Review Part 2

Total questions: 40

Worksheet time: 3hrs 20mins

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