Transcript rttSS 4.2 Ratios within Similar Triangles.pptx

SS 4.2 Ratios within Similar Triangles
1) Teaching Target: I can use equivalent ratios to
compare corresponding sides of similar triangles.
2) Homework: Inv 3-4 pkt p. 14 – Termite Puzzle
3) Warm-Up:
If the scale factor is 1.5
what are the side
lengths of the image?
(pay close attention
to the figures!)
pkt p. 13
Which triangles are similar?
For each triangle, find the ratio of the
shortest side to the longest side,
and the ratio of the
shortest side to the middle side.
A
B
C
D
Short to Mid
Short to Long
7
17.5
10.5
13
A
𝟒
𝟖
= 𝟏𝟐
𝟒
𝟕
C, D
B
𝟗
𝟏𝟑
C
𝟔 𝟏
𝟏𝟐 = 𝟐
𝟔
𝟏𝟎.𝟓
A, D
D
𝟏𝟎
𝟐𝟎
𝟏𝟎
𝟏𝟕.𝟓
A, C
= 𝟏𝟐
𝟗
𝟏𝟐
= 𝟑𝟒
none
Short to Mid
Short to Long
7
10.5
17.5
= 𝟏𝟐
𝟒
𝟕
C, D
A
𝟒
𝟖
C
𝟔 𝟏
𝟏𝟐 = 𝟐
𝟔
𝟏𝟎.𝟓
A, D
DD
𝟏𝟎
𝟐𝟎
𝟏𝟎
𝟏𝟕.𝟓
A, C
= 𝟏𝟐
A
𝟒
𝟖
= 𝟏𝟐
𝟒
𝟕
C, D
= 𝟑𝟒
none
B
𝟗
𝟏𝟑
C
𝟔 𝟏
𝟏𝟐 = 𝟐
𝟔
𝟏𝟎.𝟓
D
𝟏𝟎
𝟐𝟎
𝟏𝟎
𝟏𝟕.𝟓
= 𝟏𝟐
𝟗
𝟏𝟐
A, D
A, C
2. What do you notice about the ratios for the similar triangles?
Similar triangles have the SAME ratio!
3. What do you notice about the ratios for the non-similar triangles?
Non-similar triangles have different ratios!
Choose two similar triangles. Find the
scale factor from the smaller triangle to
the larger triangle. What information
does the scale factor give?
A to C = 1.5
C to A =
𝟐
𝟑
A
A to D = 2.5
C to D = 𝟓
𝟑
D to A = 0.4
D to C = 0.6
𝟒
𝟖
= 𝟏𝟐
𝟒
𝟕
C, D
= 𝟑𝟒
none
B
𝟗
𝟏𝟑
C
𝟔 𝟏
𝟏𝟐 = 𝟐
𝟔
𝟏𝟎.𝟓
D
𝟏𝟎
𝟐𝟎
𝟏𝟎
𝟏𝟕.𝟓
= 𝟏𝟐
𝟗
𝟏𝟐
A, D
A, C
5. Compare the information
given by the ratios of the side
lengths and the information
given by the scale factor.
Name three things this
information gives.
Similar figures have a constant scale factor and their
ratios of corresponding side lengths will be equivalent.
The scale factor gives the amount of stretching (or
shrinking) from the original figure to the image.
The ratio of adjacent side lengths within a figure gives
an indication of the shape of the original figure (and
image), since it compares measures within one figure.
SS 4.2 Ratios within Similar Triangles
Did I Reach my Learning Target?
Can I use equivalent ratios and scale factor to
compare corresponding sides of similar triangles.
Homework: Inv 3-4 pkt p. 14 – Termite Puzzle