Topic Test 5 & 6 Review Part 2

​Topic Test 5 & 6 Review Part 2

Multiple Choice

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

• Alternate interior angles are congruent.

• Corresponding angles are congruent.

• Vertical angles are congruent.

• Alternate exterior angles are congruent

Multiple Choice

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

• AAS

• ASA

• SAS

• SSS

Match

Match the following. #2

• Draw BD parallel to AC.

• m∠4+m∠2+m∠5=180∘

• ∠1≅∠4, ∠3≅∠5

• m∠1=m∠4, m∠3=m∠5

• m∠1+m∠2+m∠3=180∘

Parallel Postulate

Angle Addition Postulate and definition of straight edge

Alternate Interior Angles Theorem

Definition of congruent angles

Triangle Sum Theorem

• Parallel Postulate

• Angle Addition Postulate and definition of straight edge

• Alternate Interior Angles Theorem

• Definition of congruent angles

• Triangle Sum Theorem

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Reorder

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

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

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

• 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

• 1
• 2
• 3

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Reorder

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

• Bisect one of the angles.

• Bisect another angle.

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

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

• 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

• 1
• 2
• 3
• 4
• 5

Fill in the Blank

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

Multiple Choice

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

• SSS

• SAS

• ASA

• AAS

Multiple Choice

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

• SAS

• SSS

• Both SSS and SAS

• Not necessarily congruent

Multiple Select

Which triangles are congruent to A? #9

HINT: FIND THE THIRD ANGLE.

• none of them

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Multiple Choice

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

• 2 cm, 6 cm, 7 cm

• 5 cm, 2 cm, 5 cm

• 5 cm, 5 cm, 8 cm

• 3 cm, 10 cm, 15 cm

Multiple Choice

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

• between 8 and 15

• between 7 and 23

• less than 7, greater than 23

Multiple Choice

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

• $$5<x<16$$  

• $$4<x<14$$  

• $$4<x<17$$  

• $$3<x<17$$  

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Multiple Choice

Complete with >, < or =. #18

• >

• <

• =

• I don't know.

Multiple Choice

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

• measure of angle Y = measure of angle M

• measure of angle Y > measure of angle M

• measure of angle Y < measure of angle M

• Not enough information is given.

Multiple Choice

Choose the TRUE statement. #21

• $$KL>MN$$

• $$KL<MN$$

• $$KL=MN$$

• The above statements are all false.

Multiple Select

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

• $$2AB=AD$$  

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

• $$\overline{AC}=\overline{CE}$$  

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

Multiple Choice

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

• right

• equilateral

• isosceles

• scalene

Multiple Select

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

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

• The triangle is a right triangle.

• The triangle is an isosceles triangle.

• The triangle is an equilateral triangle.

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

Multiple Choice

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

• right

• acute

• obtuse

• equiangular

Multiple Choice

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

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

• $$y=\frac{3}{2}x+2$$  

• $$y=\frac{5}{2}x+3$$  

• $$y=2x+2$$  

• $$y=\frac{1}{3}x+2$$  

Multiple Choice

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

• (-1,2)

• (-3,2)

• (0,2)

• (1,2)

Drag and Drop

What are the coordinates of the centroid of △PQR?

(x, y) (​

Placeholder

,​

Placeholder

) #37

Drag these tiles and drop them in the correct blank above

-5

5

-6.5

6

-3

5.5