Transcript Warm-Up Exercises

Warm-Up Exercises
Groups will read pages 367-369
Group One will explain Example One on page 367 and will
explain problem 22 on page 372
Group Two will explain the Key concept on the bottom of
page 367 and example 2
Group Three will explain the two guided practice
questions on page 368
Group Four will explain example 3 on the bottom of page
368
Group Five will explain example 4 on page 369
Group Six will explain the guided practice on the bottom of
page 369
EXAMPLE
Warm-Up1Exercises
Describe a dilation
FEG is similar to
moves FEG onto
FDH. Describe the dilation that
FDH.
SOLUTION
The figure shows a dilation with
center F.
The scale factor is 2 because the ratio
of FH to FG is 20 : 10, or 2 : 1.
EXAMPLE
Warm-Up2Exercises
Describe a combination of transformations
ABC is similar to FGE. Describe a combination
of transformations that moves ABC onto FGE.
SOLUTION
A dilation with center B and scale
factor 2 moves ABC onto DBE.
3
Then a rotation of DBE with center E
moves DBE onto FGE. The angle of
rotation is equal to the measure of C.
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 1 and 2
The two figures are similar. Describe the
transformation(s) that move the blue figure onto the red
figure.
1.
2.
ANSWER
dilation with center
7
B and scale factor 3
ANSWER
2
dilation with scale factor
3
and reflection
EXAMPLE
Warm-Up3Exercises
Use transformations to show figures are not similar
Use transformations to explain why ABCDE and KLQRP
are not similar.
EXAMPLE
Warm-Up3Exercises
Use transformations to show figures are not similar
SOLUTION
Corresponding sides in the pentagons 2
are proportional with a scale factor of 3 .
However, this does not necessarily
mean the pentagons are similar.
A dilation with center A and scale
factor 2 moves ABCDE onto
3
AFGHJ. Then a reflection moves
AFGHJ onto KLMNP.
KLMNP does not exactly coincide with KLQRP, because
not all of the corresponding angles are congruent.
(Only
A and K are congruent.) Since angle measure
is not preserved, the two pentagons are not similar.
EXAMPLE
Warm-Up4Exercises
Use similar figures
GRAPHIC DESIGN A design for a party mask is made
using all equilateral triangles and a scale factor of 1 .
2
a. Describe transformations that move triangle A onto
triangle B.
b. Describe why triangles C and D are similar by using
the given information.
EXAMPLE
Warm-Up4Exercises
Use similar figures
SOLUTION
a. The figure shows a dilation
with scale factor 1
2
followed by a clockwise
rotation of 60°.
b. Triangles C and D are similar
because all pairs of
corresponding sides are
1
proportional with a ratio of
2
and all pairs of corresponding
angles of equilateral triangles
have the same measure.
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 3 and 4
Refer to the floor tile designs shown below. In each
design, the red shape is a regular hexagon.
Warm-Up
Exercises
GUIDED
PRACTICE
3.
for Examples 3 and 4
Tile design 1 is made using two hexagons. Explain
why the red and blue hexagons are not similar.
4. Tile design 2 is made using two similar geometric
shapes. Describe the transformations that move
the blue hexagon to the red hexagon.
5.
Tile design 3 shows congruent angles and sides.
Explain why the red and blue hexagons are similar,
using the given information.
6.
If the lengths of all the sides of one polygon are
proportional to the lengths of all the corresponding
sides of another polygon, must the polygons be
similar? Explain.
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 3 and 4
SAMPLE ANSWER
3.
The red hexagon has all sides congruent, but the blue
hexagon has 3 shorter sides and 3 longer sides, so
ratios of corresponding side lengths are not constant.
4. dilation followed by a rotation of 30° about the
center of the figures
5.
All angles are congruent, so angle measure is
preserved, and all side lengths are congruent in each
hexagon, so the ratio of any two corresponding side
lengths is constant.
6.
No; even though corresponding sides might be
proportional, if corresponding angles are not
congruent, the polygons are not similar.
Warm-Up Exercises
Warm-Up Exercises
An artist wants to
paint a picture. She
wants the canvas to be
a golden rectangle
with its longer
horizontal sides 31 cm
wide. To the nearest
100th of a cm, how
wide should the canvas
be?
Warm-Up Exercises
The sides of a
pentagon are 7,15, 9,
18, and 12. The
longest side of a
similar pentagon is 40.
What is the perimeter
of the similar
pentagon?
Warm-Up Exercises
Are the triangles similar? If so, write the similarity
ratio, the similarity statement, and name the postulate
or theorem that you can use to prove they are similar.
Also, explain how you can use the postulate or theorem.
If not, write not similar and explain why they are not
similar.
Warm-Up Exercises
The Sears Tower in Chicago is 1444 feet high. A model of the
tower is 48 INCHES tall. What is the ratio of the height of the
model to the height of the actual Sears Tower?