Dilations
Enlarging or reducing a figure.
What is dilation?
What is the formula we use to find the missing side for similar triangles?
BIG/SMALL = BIG/SMALL
OR
SMALL/BIG=SMALL/BIG
True or false: Similar figures have the same SHAPE, but could have different sizes.
True
180
NAME AND DESCRIBE 1 of the 3 triangle similarity theorems we've learned about in Unit 2C.
AA, SSS, SAS
When k>1, what happens?
Enlargment
DOUBLE JEOPARDY!!!!!!!!!
PLACE YOUR BID! I WILL REVEAL THE QUESTION! π
50 FEET
LOOK AT #8!!!!!!!!!!!! πππ
Triangle KLM is the pre-image of ΞKβLβMβ before a transformation.
Are the two triangles similar?
YES
In triangle ABC, angle A is 45β° and angle B is 50β°.
TRUE OR FALSE: Triangle DEG where angle D is 45β° and angle E is 85β°.
TRUE
The two triangles below are similar. Find the measure of y.
80 DEGREES
Triangle GHJ with vertices G(-2, 4), H(3, 6), and J(3, -2) is dilated by a factor
of π
π
centered at the origin. What are the coordinates of G' after the dilation?
(-1/2, 1)
LOOK AT #3!!!!!!!!!!!!! πππ
Lloyd is standing near a power line pole as shown in the figure. When his head touches the support wire, he is 2 1/2 feet from where the wire meets the ground.
If the power line pole is 17 feet tall, how tall is Lloyd?
5 FEET
CHALLENGE!!!
For an extra 300 points, select a problem from the review and work it on the board with your team. Teach it to the class in less than 2 minutes.
Challenge Accepted! 300 POINTS!!!!!!!!!!!
In triangle ABC, angle A is 45β° and angle B is 50β°.
TRUE OR FALSE: Triangle MNO where angle N is 45β° and angle O is 60β°.
FALSE
LOOK AT #10!!!!!!!!!!!!!! ππ
The two triangles below are similar. Find the measure of x.
53 DEGREES
LOOK AT # 2!!!!! πππ
Polygon MNPQ is shown on the coordinate plane. A dilation centered about the origin will be performed on the polygon.
The location of the vertex M after the dilation is (-8,6). What is the location of vertex Q after the dilation?
(-4,-4)
LOOK AT #5!!!!!!!!!!!! ππ
Triangle PQR is similar to triangle EDC.
What is the length of segment CD?
78 inches
LOOK AT #8!!!!!!!!!!!! πππ
Triangle KLM is the pre-image of ΞKβLβMβ before a transformation.
Paul said that ΞABC was dilated by a scale factor of 1.5 centered at the origin. Is Paul CORRECT?
π¨π¨π¨(If no, what is the scale factor).π¨π¨π¨
No, the scale factor is about 1.6
In triangle ABC, angle A is 45β° and angle B is 50β°.
TRUE OR FALSE: Triangle GHI where angle G is 50β° and angle I is 85β°.
TRUE
LOOK AT #11!!!!!!!!!!!!!!!! ππ
Which of the following reasons justifies Step 3?
Angle-Angle (AA) Similarity
Reflexive Property of Congruence
Vertical angles are congruent.
Corresponding angles are congruent.
Corresponding angles are congruent.
LOOK AT #7!!!!!!!!!!! ππ
In the xy-coordinate plane, ΞABC has vertices A(7,3), B(5, -1), and C(4, 5) and ΞDEF has vertices Aβ(3, 3), Bβ(2, 1), and Cβ(1.5, 4). The triangles are similar because ΞDEF is the image of ΞABC under a dilation.
Which two statements are TRUE About the transformation of ΞABC?
C. The center of dilation is at (-1, 3).
E. The scale factor is 2.
Joey built a model sailboat that is similar to his real sailboat. The triangular sail on his real boat has a base of 25 feet. If the height of the sail on his model boat is 12 inches and the base is 24 inches, what is the height of the sail on his real boat?
12 1/2 FEET
In the coordinate plane, line p has slope 8 and y-intercept (0, 5). Line r is the result of dilating line p by a factor of 4 with center (0, 3).
What are the slope and y-intercept of line r?
C. Line r has slope 8 and y-intercept (0, 11)
In triangle ABC, angle A is 45β° and angle B is 50β°.
TRUE OR FALSE: Triangle PQR where angle Q is 45β° and angle R is 50β°.
TRUE
LOOK AT #11!!!!!!!!!!!!!!!! ππ
What should be the STATEMENT FOR Step 5?
AB/AD = AE/AC