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Evidence of Understanding
I can …
I can reason to verify
and explain
theorems. (2.6)
Sample Question
“Alternate interior angles are equal when formed by
parallel lines and a transversal.”
4=complete, 3=substantial
2=developing, 1=minimal
Given: AC DE . Prove AGH  DHG .
B
C
Explain why this is true.
G
D
A
H
E
F
I can identify
characteristics of
special
quadrilaterals.
Given: Parallelogram STVW. The diagonals intersect
at X. Determine if the following statements are true or
false. Justify your response.
a. ST  VW
b. SV  TW
c. STV  TVW
d. STV is supplementary to TVW
What level is your
understanding?
mAGH  EHF because corresponding angles
formed by parallel lines are congruent.
mEHF  GHD because vertical angles are
congruent.
AGH  DHG by the transitive property.
a. True (Opposite sides of a parallelogram are
congruent.)
b. False. Diagonals of a parallelogram are not
necessarily congruent.
c. False. Adjacent angles of a parallelogram
are only congruent when it is a rectangle.
d. True. Adjacent angles of a parallelogram are
always supplementary
I can explain the
characteristics of the
midsegments of a
triangle. (5.4)
A. If the midsegment of a triangle is 18 units
A. 18x2=36 units
long, what is the measure of the base?
B. If the midsegment of triangle has a slope or ¾
B: They are parallel so ¾ will also be the slope of the
midsegment.
what is the slope of the base?
C. If the bases of a trapezoid measure 16 and 24,
C. (16+24)/2 = 20 units
how long is the midsegment?
I can use
transformations to
justify the truth of a
conjecture.(5.3, 5.5,
5.6)
Since lengths are preserved over a reflection, I know
that H ' I  HI and H ' G  HG . Since the resulting
quadrilateral has exactly two pairs of consecutive
sides that are equal, H ' IHG is a kite.
Explain how you know GHIH' forms a kite when the
scalene triangle GHI is reflected across the longest side
H
G
I
H'
Explain how you know KLEL' forms a parallellogram when the scalene
triangle KLE is rotated 180° around the midpoint of the longest side
L
K
E
L'
I can draw
Given line j is parallel to line k, what is the measure of
conclusions about
angle 1?
angle pairs formed by
parallel lines and a
transversal. (2.6)
Since angles are preserved over a rotation, I know
that mLEK  mEKL ' and mEKL  mKEL ' .
Since both of these are pairs of alternative angles
and the pairs are equal, the lines forming them must
be parallel: LE KL ' and LK EL ' . Since the triangle
was rotated over the midpoint of KE , I know that
KLE and its rotation, KL ' E form a quadrilateral. A
quadrilateral with two sets of parallel sides is a
parallelogram.
Since the 125 angle and 2 are corresponding
angles, they are equal.
Since 1& 2 are a linear pair, they are
supplementary.
125  m1  180
m1  55
125°
3
j
2
k
I can apply theorems
about parallel and
perpendicular lines.
1
Write at least four statements that can be used to
justify that j is parallel to k.
1
2
3
4
j
5
6
8
k
7
Some possible responses are shown below:
 If m1  m5 , then j k by Corresponding
Angles.
 If m3  m5 , then j k by Alternate Interior
Angles.
 If m1  m7 , then j k by Alternate Exterior
Angles.
If 4 & 5 are supplementary, then j k by SameSide Interior Angles.
I can solve problems
involving angles and
parallel lines.
Since BAD & ADC are Same-Side Interior
angles, they are supplementary.
Use what you know about parallelograms to find
mBDA .
B
C
m
74  (4x  13)  (3x  35)  180
7 x  96  180
7 x  84
x  12
mBDA  4(12)  13  35
74°
A
4x-13
r
3x+35
D
n
s
What level is your
understanding?
I can …
I can use the
exterior angle
theorem to solve
problems. (5.1, 5.2)
Sample Question
Find x and mABC .
Sample Solution
Since exterior angles of a triangle are equal to the
sum of the two remote interior angles,
A
2x°
3x+3°
C 78°
B
78  2x  3x  3
78  5x  3
75  5x
15 = x
mABC  3(15)  3
D
 48
4=complete,
3=substantial
2=developing,
1=minimal
b. Find the sum of the exterior angles of a heptagon.
a. Heptagon  7-sided polygon
Sum of Interior Angles = 180 (7-2) = 900
b. Sum of Exterior Angles = 360
c. Find the sum of the exterior angles of a kite.
c. Sum of Exterior Angles of a kite = 360
Figure ABCDEF is a regular hexagon. Find x and y.
Since the figure is a regular hexagon, the interior
angles are all congruent and the exterior angles are
all congruent.
I can find the sums
of the interior
angles and exterior
angles of a convex
polygon. (5.1, 5.2)
a. Find the sum of the interior angles of a heptagon.
I can find the
measure of interior
and exterior angles
of a convex
polygon. (5.1, 5.2)
B
C
Sum of Interior Angles = 180(6-2) = 720
y°
D
A
x = Each interior angle =
720
 120
6
Sum of Exterior Angles = 360
x°
F
E
y = Each exterior angle =
360
 60
6