Download Geometry 2: Triangle Similarity Part 1 REVIEW Key G

Geometry 2: Triangle Similarity Part 1 REVIEW
Key
G-CO.2. Learning Target: I can compare transformations
that preserve distance and angle measures to those that
do not.
1. Compare the two transformations shown below, with
respect to distance and angle measures.
Transformation (a):
In (b), the transformation stretches the figure only in
the horizontal direction and does not preserve the
angle measurements, thus the figures are not similar.
G.CO-10. Learning Target: I can prove that the
segment joining midpoints of two sides of a triangle is
parallel to and half the length of the third side.
2. The coordinates of the vertices of a triangle are K(2,3),
L(-2,-1), and M(5,1).
(a) Find the coordinates of N, the midpoint of KM , and
P, the midpoint of LM .
2+5 3+1
, 2 )
2
In (a), the transformation (translation) is a rigid
motion so the lengths of all corresponding sides and
the size of all corresponding angles are congruent.
Transformation (b):
−2+5 −1+1
, 2 )
2
𝑁: (
𝑃: (
𝑁: (3.5,2)
𝑃: (1.5,0)
(b) Show that NP || KL .
𝑚𝑁𝑃
̅̅̅̅ =
2−0
3.5−1.5
= =1
2
2
3+1
4
𝑚̅̅̅̅
𝐾𝐿 = 2+2 = 4 = 1
(c) Show that NP = ½ KL.
2
2
𝑑̅̅̅̅
𝑁𝑃 = √(3.5 − 1.5) + (2 − 0) = √8 = 2√2
2
2
𝑑̅̅̅̅
𝐾𝐿 = √(2 + 2) + (3 + 1) = √32 = 4√2
G-SRT.1. Learning Target: I can verify the following
statements by making multiple examples: a dilation of a
line is parallel to the original line if the center of dilation
is not on the line; a dilation of a line segment changes the
length by a ratio given by the scale factor.
3. (a) Graph DE with D(-3,-4) and E(4,-4). Then graph
its dilation using the origin as the center and a scale factor
of 1.5. Label the dilation D ' E ' .
G-SRT.2.Learning Target: I can decide if two figures
are similar based on similarity transformations. I can
use similarity transformations to explain the meaning of
similar triangles as the equality of all corresponding
pairs of angles and the proportionality of all
corresponding pairs of sides.
4. Su, who is 5 feet tall, is standing at point D in the
drawing below. The top of her head is at point E. A tree
in the yard is at point B with the top of the tree at point C.
Su stands so her shadow meets the end of the tree's
shadow at point A.
Part A: Which triangles are similar?
Part B: How do you know?
The triangles are similar because all corresponding
angles are congruent.
𝑫
Part C: What is the ratio of the triangles?
𝑬
𝑫′ (−𝟒. 𝟓, −𝟔)
𝑬′ (𝟔, −𝟔)
5
8
Part D: Find the height of the tree.
15 ft
5.Find the value of x, y, and the measure of angle P.
(b) Find the length of the dilated line segment.
𝐷 ′ 𝐸 ′ = 𝟏𝟎. 𝟓
(c) Find the value of the ratio of the dilated segment to
the length of the original segment.
10.5 1.5
=
7
1
The ratio of the length of the dilated segment to the
length of the original segment is 1.5: 1.
21
2
x6
y
P  860
6. Use side length proportionality to determine if the
triangles are similar.
𝟑
𝟓
𝟖
=
=
𝟕. 𝟓 𝟏𝟐. 𝟓 𝟐𝟎
𝟏
𝟏
𝟏
=
=
𝟐. 𝟓 𝟐. 𝟓 𝟐. 𝟓
The triangles are similar
G-SRT.3. Learning Target: I can establish the AA
criterion by looking at multiple examples using similarity
transformation of triangles.
7. Use the Angle-Angle Similarity Postulate to determine
which pair of triangles is not similar.
A) .
C).
B).
D).