Download Worksheet 5.05

Worksheet 5.05
Name:______________________________
In problems 1 - 4, select the correct multiple choice response.
1.
In the figure ABC is a right triangle
A
Assume temporarily that mC > 90°.
It follows that mC + mB > 180°. This
contradicts the triangle sum theorem that states
the sum of all 3 angles in a triangle sums to 180°.
What conclusion can be drawn from this contradiction?
a.
ABC is a not right triangle
b.
mC > 90°
c.
mC
d.
mB  90°
90°
In problems 11 – 13, select the correct multiple choice response.
2.
In the figure LMP is an isosceles triangle with LM  LP
Let us assume that M
C
B
L
P . Then it follows that
LM
LP since if angles aren’t congruent then sides opposite
aren’t congruent. What conclusion can be drawn from this
contradiction?
M
P
P
a.
M  P
b.
M
c.
LM
d.
LMP is not an isosceles triangle
LP
K
3.
In the figure mL = 70° and mK = 45°
45°
70°
1
L
D
Assume temporarily that m 1  115°. Then it
follows that mL and mK cannot be 70° and 45° since this contradicts the Exterior
Angle Theorem that states that the measure of an exterior angle of a triangle is equal to
the sum of the measures of the two nonadjacent interior angles. What conclusion can be
drawn from this?
a.
mL  70°
b.
m 1 = 115°
c.
mK  45°
d.
The exterior angle theorem is false.
t
1
4.
In the figure, m 1 = 110° and m 2 = 110°
p
m
2
Let us assume that line p is not parallel to line m. Then it
follows that m 1 and m 2 cannot each be 110° since this contradicts
the Alternate Exterior Angles Converse Theorem that states that if two lines
are cut by a transversal so that alternate exterior angles are congruent then the lines
must be parallel. What conclusion can be drawn from this?
a.
line p is parallel to line m
b.
m 1  110°
c.
m 2  110°
d.
line p is not parallel to line m