Download Angle Inequalities, Triangle Congruence, Points of Concurrency

REVIEW
Standard: Angles
MM1G. Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.
b. Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.
_________________1. The sides of a triangle are 15, 8 and x. What are the possible values for x?
_________________2. In CAT , m C is 51 and m T is 63. What is the longest side of the triangle?
__________________3. Two sides of a triangle have lengths 3 and 12. The possible lengths of the third side are ______ .
__________________4. Write the angles in order from largest to smallest.
B
9
6
A
_________________5.
C
7
Find the measure of x.
80
130
6.
x
Draw triangle PHS and label the angles accordingly: mN  98, mH  65. Find the missing angle.
Then list the sides in order from least to greatest.
______ , _______ , _______
7.
Draw triangle XYZ and label the sides accordingly. XY = 22, YZ = 42, XZ = 31. List the angles in order
from least to greatest.
_______ , _______ , _______
8.
Describe the possible lengths of the third side of the triangle given the lengths of the other two sides: 25 yd,
36 yd.
9.
Is it possible to construct a triangle with the given side lengths: 53, 53, 107 ? If not, explain why not.
Standard: Triangle Congruence
MM1G3. Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.
c. Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).
________1.
How do you know the triangles are congruent? Write a congruence
Statement.
A
________2.
E is the midpoint of AC and BD . How do you know the triangles
are congruent? Write a congruence statement.
E
D
B
A
C
________3.
What are the five ways (short cuts) to prove the two triangles are congruent?
Decide whether enough information is given to prove that the triangles are congruent. If there is enough
information, state the congruence postulate or theorem you would use. (SSS, SAS, ASA, AAS, HL)
11
12
13
14
Answer_____________
15
Answer_____________
16
Answer_____________
Answer_____________
Answer_____________
Answer_____________
State the third congruence that is needed to prove that ABC  XYZ using the given postulate or theorem:
17. Given: A  X , C  Z , and ____  ____
~Use the AAS Congruence Theorem
18. Given: A  X , AC  XZ , and ____  ____
~Use the ASA Congruence Postulate
19. Given: AC  XZ , C  Z , and ____  ____
~Use the SAS Congruence Theorem
Standard: Points of Concurrency
MM1G3. Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.
e. Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.
1. Which points of concurrency may lie outside the triangle?
2. Which points of concurrency are always inside the triangle?
3. Which point of concurrency is equidistant from the vertices of the triangle?
4. Which point of concurrency is equidistant from the sides of the triangle?
5. Which point of concurrency is 2/3 the distance from the vertex to the side?
Name the special segment drawn.
_______________________6.
_______________________7.
_______________________8.
_______________________9.
What is the point of concurrency for the:
10. altitudes
11. angle bisectors
12. medians
13. perpendicular bisectors
Sample Bonus Questions!
In the diagram, the perpendicular bisectors of triangle ABC meet at point G and are shown
dashed. Find the indicated measure.
Find BG
B
15
Find AC
D
10
A
E
G
12
13
C
F
Given the diagram as shown, list the segments, XY , YZ, XZ, WZ, and YW , in order of size
starting with the smallest.
X
Y
30
W
Z