Download Geometry Chapter 5 Review

Geometry Chapter 5 Review
Relationships Within Triangles
Name:____________________________
SECTION 5.1: Midsegments of Triangles
1. A midsegment of a triangle is a segment that connects the _____________________ of two sides.
A midsegment is _____________________________ to the third side and _________ its length.
2. X is the midpoint of UV . Y is the midpoint of UW .
If VW = 110, find XY .
4. B is the midpoint of
and D is the midpoint of
3. Find the value of x.
Solve for x, given BD = 6x + 1 and AE = 13x – 7.
C
B
A
D
E
5. Given the perimeter of FGE is 35 find the value of x if AB = 2x +16, CB = 8x+6 and AC = 4x-8.
6. Solve for x.
SECTION 5.2: Bisectors in Triangles
7. A point is on the perpendicular bisector of a segment if and only if it is ____________________
from the endpoints of that segment.
A point is on the angle bisector of an angle if and only if it is _______________________ from the
________________________________ of the angle.
8. From the information given in the picture, how is
AC related to BD ? Find AB
9. Find JM.
.
10.
11. Use the figure below to answer the
following questions:
a. What is the measure of XV?
b. What is the measure of XY?
c. Classify  WXZ by its sides.
12. Q is equidistant from the sides of
T
|
|
(4
x
+
3)
°
Q
(8x – 5)°
S
R
Find
The diagram is not to scale.
SECTION 5.3: Congruent Lines, Medians, and Altitudes
13. The medians of a triangle intersect at the _______________.
The circumcenter of a triangle is equidistant from the _____________ of the triangle.
An altitude of a triangle starts at a ____________ and is _______ to the opposite side.
The incenter is the point of concurrency for the ______________________ of a triangle.
14. Determine whether AB is a perpendicular bisector, altitude, angle bisector, median, or none.
a.
b.
15. Find the coordinates of the circle circumscribed about the given triangle.
16. Find the coordinates of the circumcenter and the orthocenter of the traingle.
17. Sketch and label the medians of the triangle below. What is the point of concurrency called?
18. Create  CUB with vertices C (4, 6), U(4, -2) and B(-6, 6) on the graph above.
a. What are the coordinates of the circumcenter?
b. What are the coordinates of the orthocenter?
19. In the diagram below:
AF is a(n) ______________________ .
BD is a(n) ______________________.
CE is a(n) ______________________.
SECTION 5.4: Inverse, Contrapositives, and Indirect Reasoning
20. Consider the conditional statement:
If it is snowing, then it is cold outside.

What is the converse of the conditional (from Chapter 2)?

What is the inverse of the conditional?

What is the contrapositive of the conditional?

Circle which are true:
conditional, converse,
21. Write the first step for the indirect proof of the following…
Given: LMN
Prove: LMN has at most 1 right angle.
negation, inverse, contrapositive
22. Select the two statements that contradict eachother.
SECTION 5.5: Inequalities in Triangles
C
23. Name the largest angle of
The diagram is not to scale.
a. Two angles are the same size and smaller than the third.
b.
c.
d.
5
A
6
7
24. List the angles in order from smallest to largest.
25. List the sides in order from largest to smallest.
26. Which segment is the largest? Which segment is the smallest?
27. Is it possible to have a triangle with sides of the given lengths?
2cm, 3cm, 6cm
4in, 4in, 8in
4.5ft, 6ft, 11ft
B
28. Which three lengths could not be the lengths of the sides of a triangle?
a. 9 cm, 22 cm, 15 cm
c. 12 cm, 5 cm, 17 cm
b. 21 cm, 17 cm, 6 cm
d. 10 cm, 15 cm, 24 cm
29. A triangle has the following angle measures, list the sides in order of largest to smallest.
m<T = 4x + 15
m<R = 7x + 4
m<S = 5x + 1
30.
and
List the sides of
in order from smallest to largest.
31. Where do all medians meet (in, on, out)? What is this called?
32. Where do all angle bisectors meet (in, on, out)? What is this called?
33. Where do all perpendicular bisectors meet (in, on, out)? What is this called?
34. Where do all altitudes meet (in, on, out)? What is this called?
35. The measure of the exterior angle is EQUAL, GREATER THAN, or LESS THAN the sum of the remote
interior angles?
36. A triangle has sides 2 and 8 inches. Write an inequality to show the range of values for the third side.
37. Two sides of a triangle have lengths 32 and 21. Write an inequality statement that describes the values for
the possible lengths of the third side.
38. Respond to the following questions with always, sometimes, never.
a. A true statement has a false negation.
b. An altitude of a triangle is also an angle bisector.
c.
The medians of an acute triangle meet inside the triangle.
d. The midsegment of a triangle is congruent to the side it is parallel to.
e. The angle bisectors of a triangle are concurrent at one point.