Name ______________________________________________________			Period _______

Chapter 6 Review Makeup

	1.	Find BC.

	2.	Find AB. 

	3.	In the diagram,  bisects  Find CD .

	4.	Write an equation of the perpendicular bisector of the segment with endpoints  and .

	5.	In the diagram of the formal garden, the east-west path is perpendicular to the north-south path and . Which theorem allows you to conclude that ?

	6.	When a king truss is built correctly, point P lies on the bisector of , as shown in the diagram.  How can a carpenter use the supports  and  to make sure that P is in the correct position? 

	7.	A ribbon is used to hang a picture on a nail at point N. How can you use the two lengths of ribbon  and  to make sure the picture is straight and centered under the nail?

	8.	An electrician has a diagram to erect a street lamp in the park so that is equidistant from Main Street and Park Avenue and also equidistant from the statue and fountain.  How does the electrician’s plan ensure that the street lamp is in the proper location at point P? 

	9.	The diagram shows a piece of wood for one side of a shelf.  Point P is the center of a hole for a dowel rod that is to be drilled 5 centimeters from sides  and . You draw segment . Can you conclude that the segment bisects ? Explain. 

	10.	Find the coordinates of the circumcenter of  with vertices , , and .

	11.	In , N is the incenter, , and . Which of the measures are possible lengths of NG? 

		

	

	12.	Three cities are located on a map, as shown.  An engineer wants to erect a telecommunications tower so that it is the same distance from each city.  Explain how the engineer can use the map to locate the tower.

	13.	You are drilling a hole in the triangular birdhouse shown. You want the hole to be the same distance from all three sides. Where should you drill the hole?  Explain your reasoning.

	14.	In , point P is the centroid, and . Find LP  and BL.

	15.	In , point P is the centroid, and . Find AP  and AN .

	16.	The Park and Recreation department wants to add some sidewalks to the park. The fountain F is located at the park’s centroid and is 130 feet from entrance C. How many feet of sidewalk are needed to connect the fountain to the petting zoo?

	17.	Tell whether the orthocenter is inside, on, or outside the triangle with vertices , , and . Then find the coordinates of the orthocenter.

	18.	Tell whether the orthocenter is inside, on, or outside the triangle with vertices , , and . Then find the coordinates of the orthocenter.
	19.	A company builds trusses to support structures. In the truss shown below, the support  is the midsegment of . Find the value of x.

	20.	You install fencing around your large triangular garden. Then, you divide it into four small triangular gardens by connecting the midpoints of each side of the triangle with fencing. How many feet of fencing do you need?

In the stained glass image,  and . Copy and complete the statement.

	21.	
	22.	
	23.	
	24.	
	25.	

	26.	List the sides of  from shortest to longest.

	27.	List the sides of  from shortest to longest.

	28.	A triangle has one side that measures 3 feet and another side that measures 10 inches. Which are possible side lengths of the third side? 

		

Match the set of segment lengths below with its description.
a.	 is the largest angle in .	c.	 is the largest angle in .	
b.	 is the largest angle in .	d.	The segments do not form a triangle.

	29.	, , 

	30.	, , 

	31.	Is it possible to construct a triangle with sides of  lengths 55, 15, and 37?   If not, explain why not.

Write the first step in an indirect proof of the given statement.

	32.	If  then 

	33.	In , if  then 

	34.	Given    
Prove   

STATEMENTS	REASONS	
1. 	1. Given	
2. 	2. Definition of congruent segments	
3. 	3. 	
4. 	4. Subtraction Property of Equality	
5. 	5. 	

	35.	Complete the flowchart proof. Then write a two-column proof.

Given   , , 
Prove   

Chapter 6 Review Makeup
Answer Section

	1.	ANS:	
BC = 24

PTS:	1	DIF:	Level 1	REF:	Math2 Sec. 6.2	
KEY:	perpendicular bisector	NOT:	Example 1

	2.	ANS:	
AB = 27

PTS:	1	DIF:	Level 1	REF:	Math2 Sec. 6.2	
KEY:	perpendicular bisector	NOT:	Example 1

	3.	ANS:	
CD  = 2

PTS:	1	DIF:	Level 1	REF:	Math2 Sec. 6.2	
KEY:	angle bisector			NOT:	Example 3

	4.	ANS:	

PTS:	1	DIF:	Level 2	REF:	Math2 Sec. 6.2	
KEY:	perpendicular bisector	NOT:	Example 5

	5.	ANS:	
Perpendicular Bisector Theorem

PTS:	1	DIF:	Level 3	REF:	Math2 Sec. 6.2	
KEY:	perpendicular bisector | application			NOT:	Example 2-3

	6.	ANS:	
The supports can be installed so that  and . Then, by the Converse of the Angle Bisector Theorem, point P is on the bisector of .

PTS:	1	DIF:	Level 2	REF:	Math2 Sec. 6.2	
KEY:	angle bisector | application	NOT:	Example 4

	7.	ANS:	
You need to make .

PTS:	1	DIF:	Level 2	REF:	Math2 Sec. 6.2	
KEY:	angle bisector | application	NOT:	Example 4

	8.	ANS:	
Any point on the bisector of the angle formed by the two roads is equidistant from the two roads. Any point on the perpendicular bisector of the segment between the statue and the fountain is equidistant from the two objects. So, the proper location for the streetlight is the intersection of the two bisectors.

PTS:	1	DIF:	Level 3	REF:	Math2 Sec. 6.2	
KEY:	angle bisector | perpendicular bisector | application	NOT:	Example 4

	9.	ANS:	
yes; Point P is in the interior of  and it is equidistant from sides  and . So, P lies on the bisector of .

PTS:	1	DIF:	Level 1	REF:	Math2 Sec. 6.2	
KEY:	angle bisector | application	NOT:	Example 4

	10.	ANS:	

PTS:	1	DIF:	Level 1	REF:	Math2 Sec. 6.3	
KEY:	circumcenter			NOT:	Example 2

	11.	ANS:	A, B	PTS:	1	DIF:	Level 2	REF:	Math2 Sec. 6.3
KEY:	incenter	NOT:	Example 3

	12.	ANS:	
The engineer can connect the cities to draw a triangle and draw three perpendicular bisectors of the triangle. The point where the perpendicular bisectors meet, the circumcenter, should be the location of the telecommunications tower.

PTS:	1	DIF:	Level 2	REF:	Math2 Sec. 6.3	
KEY:	circumcenter | application	NOT:	Example 1

	13.	ANS:	
You should drill the hole at the incenter of the birdhouse because the incenter is equidistant from the sides of the triangle by the Incenter Theorem.

PTS:	1	DIF:	Level 2	REF:	Math2 Sec. 6.3	
KEY:	circumcenter | incenter | application			NOT:	Example 4-2

	14.	ANS:	

PTS:	1	DIF:	Level 1	REF:	Math2 Sec. 6.4	
KEY:	centroid	NOT:	Example 1

	15.	ANS:	

PTS:	1	DIF:	Level 1	REF:	Math2 Sec. 6.4	
KEY:	centroid	NOT:	Example 1

	16.	ANS:	
260 ft

PTS:	1	DIF:	Level 1	REF:	Math2 Sec. 6.4	
KEY:	centroid | application		NOT:	Application-1		

	17.	ANS:	
on; 

PTS:	1	DIF:	Level 2	REF:	Math2 Sec. 6.4	
KEY:	orthocenter	NOT:	Example 3

	18.	ANS:	
inside; 

PTS:	1	DIF:	Level 2	REF:	Math2 Sec. 6.4	
KEY:	orthocenter	NOT:	Example 3

	19.	ANS:	
19 ft

PTS:	1	DIF:	Level 1	REF:	Math2 Sec. 6.5	
KEY:	midsegment of a triangle | application		NOT:	Example 3

	20.	ANS:	
132 ft

PTS:	1	DIF:	Level 2	REF:	Math2 Sec. 6.5	
KEY:	midsegment of a triangle | application		NOT:	Example 5-2

	21.	ANS:	

PTS:	1	DIF:	Level 1	REF:	Math2 Sec. 6.5	
KEY:	midsegment of a triangle | application		NOT:	Example 4

	22.	ANS:	

PTS:	1	DIF:	Level 1	REF:	Math2 Sec. 6.5	
KEY:	midsegment of a triangle | application		NOT:	Example 4

	23.	ANS:	

PTS:	1	DIF:	Level 1	REF:	Math2 Sec. 6.5	
KEY:	midsegment of a triangle | application		NOT:	Example 4

	24.	ANS:	

PTS:	1	DIF:	Level 1	REF:	Math2 Sec. 6.5	
KEY:	midsegment of a triangle | application		NOT:	Example 4

	25.	ANS:	

PTS:	1	DIF:	Level 1	REF:	Math2 Sec. 6.5	
KEY:	midsegment of a triangle | application		NOT:	Example 4

	26.	ANS:	
, , 

PTS:	1	DIF:	Level 1	REF:	Math2 Sec. 6.6	
KEY:	angles and sides of a triangle	NOT:	Example 4

	27.	ANS:	
, , 

PTS:	1	DIF:	Level 1	REF:	Math2 Sec. 6.6	
KEY:	angles and sides of a triangle	NOT:	Example 4

	28.	ANS:	A, D	PTS:	1	DIF:	Level 2	REF:	Math2 Sec. 6.6
KEY:	side lengths of a triangle	NOT:	Example 5

	29.	ANS:	D	PTS:	1	DIF:	Level 2	REF:	Math2 Sec. 6.6
KEY:	angles and sides of a triangle	NOT:	Combined Concept	

	30.	ANS:	B	PTS:	1	DIF:	Level 2	REF:	Math2 Sec. 6.6
KEY:	angles and sides of a triangle	NOT:	Combined Concept	

	31.	ANS:	
no;  

PTS:	1	DIF:	Level 2	REF:	Math2 Sec. 6.6	
KEY:	side lengths of a triangle	NOT:	Example 5

	32.	ANS:	
Assume temporarily that 

PTS:	1	DIF:	Level 1	REF:	Math2 Sec. 6.6	
KEY:	indirect proof			NOT:	Example 1

	33.	ANS:	
Assume temporarily that  is not congruent to 

PTS:	1	DIF:	Level 1	REF:	Math2 Sec. 6.6	
KEY:	indirect proof			NOT:	Example 1

	34.	ANS:	
; Substitution Property of Equality; ; Division Property of Equality

PTS:	1	DIF:	Level 1	REF:	Math2 Sec. 6.1	
KEY:	two-column proof		NOT:	Example 1

	35.	ANS:	
;  ; Reflexive Property of Congruence; Right angles are congruent.; ; Corresponding parts of congruent triangles are congruent.
STATEMENTS	REASONS	
1. , , 	1. Given	
2.  and  are right angles	2. Definition of perpendicular lines	
3. 	3. Right angles are congruent.	
4. 	4. Reflexive Property of Congruence	
5. 	5. SAS Congruence Theorem	
6. 	Corresponding parts of congruent triangles are congruent.	

PTS:	1	DIF:	Level 1	REF:	Math2 Sec. 6.1	
KEY:	two-column proof | flowchart proof			NOT:	Example 3