Medians and Midsegments

​Topic Test 5 & 6 Review Part 3

Multiple Select

Which is true about any midsegment in a triangle?

(Select all that apply.) #2

• The midsegment is parallel to its corresponding side.

• The midsegment is perpendicular to its corresponding side.

• The midsegment is half as long as its corresponding side.

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

• The midsegment is twice as long as its corresponding side.

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Multiple Choice

What would be the reason for the final step? #15

• AAS

• ASA

• SSS

• SAS

Match

Match the following. #7

• 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

Dropdown

What is the reason for # 5? ​

Select answer

What is the reason for #6? ​

Select answer

What is the reason for #7? ​

Select answer

​#29

Match

Match the following. #30

• C is the midpoint of  $$\overline{AE}$$  

• $$\overline{AE}$$  ≅ $$\overline{EC}$$  

• ∠BCA≅∠DCE

• $$\overline{BC}$$  ≅ $$\overline{DC}$$  

• △ABC≅△EDC

  and

  ∠A≅∠E

Given 1

Def. of Midpoint

Vertical Angle Theorem

Given 2

SAS

CPCTC

• Given 1

• Def. of Midpoint

• Vertical Angle Theorem

• Given 2

• SAS

  CPCTC

Multiple Choice

Fill in statement #3. #3

• $$\overline{AC}\ \cong\ \overline{AC}$$

• $$\overline{AC}\ \cong\ \overline{CA}$$

• $$\angle BAC\cong\angle DAC$$

• $$\angle B\cong\angle D$$

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Dropdown

The circumcenter of a triangle is the point of concurrency of the ​

Select answer

of a triangle. #6

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Reorder

Reorder the steps for constructing a circumcenter of a triangle. #4

• 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. #5

• 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!

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5

• 1
• 2
• 3
• 4
• 5

Multiple Choice

Bermuda, Florida, and Puerto Rico make a triangle.

From Bermuda to Florida it is 20 miles, from Florida to Puerto Rico is 34 miles, and from Puerto Rico to Bermuda it is 42 miles.

Order the angles of the triangle from least to greatest. #11

• $$\angle B,\angle F,\angle PR$$  

• $$\angle F,\angle B,\angle PR$$  

• $$\angle PR,\angle B,\angle F$$  

• $$\angle F,\angle PR,\angle B$$  

Multiple Choice

Which of the following could NOT be lengths of the sides of a triangle? #12

• 6ft, 2ft, 9ft

• 8ft, 9ft, 10ft

• 8ft, 8ft, 8ft

• 10ft, 5ft, 14ft

Multiple Select

Select all of the following that could form a triangle. #13

• 10cm, 8cm, 12cm

• 5ft, 9ft, 11ft

• 20, 3, 14

• 7in, 7in, 1in

Multiple Choice

$$\Delta LMN\ has\ vertices\ \left(\ 0,\ 12\right)\left(5,\ 7\right),\left(4,5\right).\ Find\ the\ centroid.$$  #17

• ( 3, 8 )

• ( 9 , 24) 

• ( 1 , 0 ) 

• ( 20 , 35 )

Multiple Choice

The vertices of the triangle in the diagram below are A(7,9), B(3,3), and C(11,3). What are the coordinates of the centroid of ABC? #22

• (5,6)

• (7,3)

• (7,5)

• (9,6)

Multiple Choice

Miles has 5 straws of different lengths and he wants to construct a triangle out of the straws.

Which straws should he use to form the triangle? #21

• pink, orange, blue

• yellow, blue, orange

• green, yellow, and pink

• blue, yellow, green

Multiple Select

Select the congruent triangles. #25

Fill in the Blanks

Multiple Choice

$$Find\ the\ measure\ of\ \angle\ CAB$$  . #28

• $$13\degree$$  

• $$41\degree$$  

• $$87\degree$$  

• $$52\degree$$  

Multiple Choice

Which rule explains why these triangles are congruent? #32

• SAS

• ASA

• AAS

• SSS

Multiple Choice

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

A(9, 5), B(2, 5), C(4, 1) #33

• $$y=\frac{3}{2}x+2$$  

• $$y=\frac{5}{2}x+3$$  

• $$y=2x+2$$  

• $$y=\frac{1}{3}x+2$$  

Multiple Choice

The perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. #35

• True

• False

Multiple Choice

What is a perpendicular bisector of a segment? #36

• A line that crosses through the midpoint of the segment at right angles

• A line that crosses through the midpoint of the segment

• A line that crosses the segment at a 90 degree angle

• A line that is parallel to the given segment

Multiple Choice

Two sides of a triangle have side lengths of 17 meters and 12 meters.  What is the range of possible lengths for the third side? #37

• 12 < x < 17

• 12 < x < 29

• 5 < x < 17

• 5 < x < 29

Multiple Choice

Complete with >, < or =. #41

• >

• <

• =

• I don't know.