Download Group work: (Do not write on this package). Instructions: 1) The

Group work: (Do not write on this package).
Instructions:
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
The whole group will present only one answer copy.
In your group, choose a recorder, a time keeper/presenter and a reader.
Your group will lose one point after each warning.
Your group will receive a zero for any number copied from another group.
The teacher can give helpful suggestions but cannot solve the problems for you.
All steps must be shown clearly.
The rubric will be provided in class.
Write your names clearly at the top of your copy.
Group presentation will be done through ballot.
The teacher will also grade your entire copy.
This constitutes 50% of your grade.
Part A:
1. Can you conclude the triangles are congruent? Justify your answer.
2. Based on the given information, can you conclude that
Given:
,
3. Sketch
.
? Explain.
, and
and
so that
,
, and
, but
is NOT congruent to
4. Is there enough information to prove the two triangles congruent? If yes, write the congruence statement
and name the postulate you would use. If no, write not possible and tell what other information you would
need.
Q
|
|
(
)
S
P
R
5. For
and
6. Is
,
by ASA.
,
, and
. Explain how you can prove
by HL? If so, name the legs that allow the use of HL.
P
Q
S
R
7. Separate and redraw
and
A
B
D
C
. Identify any common angles or sides.
8. Name a pair of triangles in the figure and state whether they are congruent by SSS, SAS, ASA, AAS, or
HL.
Given:
,
N
O
M
9. In the figure,
P
,
, and
. Prove that
.
10. Complete the proof by providing the missing reasons.
Given:
Prove:
,
C
D
B
E
A
Statement
1.
2.
3.
4.
5.
,
, and
are right angles
11. Write a two column proof to show that
Given:
and
B
D
C
A
E
12. Write a two-column proof.
Given:
and
Prove:
B
D
C
A
E
13. Write a two-column proof:
Reason
1. Given
2. Definition of perpendicular segments
3. ?
4. ?
5. ?
.
Given:
Prove:
B
C
A
D
14. Is there enough information to prove the two triangles congruent by AAS? If yes, write the congruence
statement and explain. If no, write not possible and tell what other information you would need.
(
Given:
A
B
C
(
D
15. Guy wires of equal length anchor a vertical post to the flat ground. The guy wires are attached to the post
at the same height. Explain why the guy wires reach the ground at the same distance from the base of the
post.
16. It appears from the name of the HL Theorem that you actually need to know that only two parts of two
triangles are congruent in order to prove two triangles congruent. Is this the case?
Part B:
1. Give the missing reasons in this proof of the Alternate Interior Angles Theorem.
Given:
Prove:
2. State the missing reasons in this proof.
Given:
Prove:
q
1 2
3 4
7
p
5 6
8
r
3. Find the measure of each interior and exterior angle. The diagram is not to scale.
5
4
122 o
6
1
2
8
3
9
7
4. Find the measures of an interior angle and an exterior angle of a regular polygon with 6 sides.
5. Find the values of the variables. Show your work and explain your steps. The diagram is not to scale.
o
31
x
w
v
y
o
68
z
6. For a regular n-gon:
a. What is the sum of the measures of its angles?
b. What is the measure of each angle?
c. What is the sum of the measures of its exterior angles, one at each vertex?
d. What is the measure of each exterior angle.
e. Find the sum of your answers to parts b and d. Explain why this sum makes sense.
7. Justify the statement algebraically.
In a triangle, if the sum of the measures of two angles is equal to the measure of the third angle, then
the triangle is a right triangle.
8. Is each figure a polygon? If yes, describe it as concave or convex and classify it by its sides. If not, tell
why.
a.
b.
c.