Name: ______ Period _________ 2/17/12 – 3/2/12 G-PreAP U NIT NIT 12: S 12: S IMILARITY IMILARITY I can define, identify and illustrate the following terms: Dilation Scale Factor Extremes Means Similarity Statement Scale Drawing Enlargement Reduction Ratio Proportion Cross products Indirect measurement Similarity ratio
16
Embed
Name: - Humble Independent School District / Overvie · Web view7-3: Triangle Similarity & 7-4: Applications and Problem Solving I can use the triangle similarity theorems to determine
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Name: ______ Period _________ 2/17/12 – 3/2/12 G-PreAP
UUNITNIT 12: S 12: SIMILARITYIMILARITY
I can define, identify and illustrate the following terms: DilationScale FactorExtremesMeans
Dates, assignments, and quizzes subject to change without advance notice.
Monday Tuesday Block Day Friday13
12- 4 and 12 – 5Compositions and
Symmetry
1412-7
Dilations
15/16ReviewTTESTEST 11 11
177-1
Ratios, Proportions, and Problem Solving
20
No School
217-2
Similar Polygons
22/237-3 & 7-4
Triangle Similarity & Applications
QUIZ 1
247-5
Proportional Relationships
27 7-6
Dilations & Similarity in the Coordinate Plane
288-1
Geometric MeanQUIZ 2
29/1ReviewTTESTEST 12 12
2
Friday, 2/17
7-1: Ratio and Proportion
I can write a ratio. I can write a ratio expressing the slope of a line. I can solve a linear proportion. I can solve a quadratic proportion.
PRACTICE: Pg 458 #8-13, 17-29
Tuesday, 2/21
7-2: Similar Polygons
I can use the definition of similar polygons to determine if two polygons are similar. I can determine the similarity ratio between two polygons.
PRACTICE: Pg 465 #7-20, 27-30 Ratio Problems Worksheet
Wednesday, 2/22 or Thursday, 2/23 QUIZ 1: 7-1 & 7-2
7-3: Triangle Similarity & 7-4: Applications and Problem Solving
I can use the triangle similarity theorems to determine if two triangles are similar. I can use proportions in similar triangles to solve for missing sides.
I can use the triangle proportionality theorem and its converse. I can use the Triangle Angle Bisector Theorem. I can set up and solve problems using properties of similar triangles.
7-6: Dilations & Similarity in the Coordinate Plane
I can use coordinate proof to prove figures similar. I can apply similarity in the coordinate plan.
PRACTICE: Pg 498 #4-7, 11-14, 21-24
Tuesday, 2/28 QUIZ 2: Similar Triangles (7-3 through 7-6)
Geometric Mean
I can use geometric mean.PRACTICE: Geometric Mean Worksheet
Wednesday, 2/29 or Thursday, 3/1
Review
Test 12: Similarity I can use ratios and proportions to show figures are similar or solve problems with similar figures.
PRACTICE: Review Worksheet; Pg 504 – 507 has even MORE practice if you want it.
Dilations as Proportions Notes
Ex) Rectangle CUTE was dilated to create rectangle UGLY. Find the length of LY.
C U
TE
8 cm3 cm
U G
LY7.5 cm
Ex) Determine which of the following figures could be a dilation of the triangle to the right. (There could be more than one answer)
1. Find the length of after the dilation.
2. Which of the following could NOT be an enlargement or reduction (dilation) of the original painting shown at right?
A B
C D
16 in.
6 in. 6 in.
2.25 in.
20 in.
10 in.
8 in.
3 in.
30 in.
5 in.
A B C D
C′
A
C
A′
BB′
6 m10 m4 m
12 in
8 in
13 in
9in
18 in
12 in
15 in
10 in
6 in
4 in
Ratio ProblemsWrite the equation for each and solve. Show all work.
1. One angle of a triangle measures 18º. The other two angles are in the ratio of 4:5. Find the measures of the angles.
2. The vertex angle and the one base angle of an isosceles triangle are in the ratio of 7:4. Find the measures of the 3 angles.
3. The sides of a triangle have the ratio of 7:9:12. The perimeter of the triangle is 420. Find the length of each side.
4. Two consecutive angles of a parallelogram are in a ratio of 7:3. Find the measures of the angles.
5. The angles of a pentagon are in a ratio of 7:6:5:5:4. Find the measures of each angle.
6. One angle of a hexagon is 120º. The other angles are in the ratio of 11:9:8:7:5. Find the measures of the angles.
7. The sides of a quadrilateral are 5, 7, 4, and 8 cm. If the shortest side of a similar quadrilateral is 10cm, what is the length of the longest side?
8. If a rectangular I.D. card is 4cm x 8cm (l x w) is enlarged so that its new perimeter is 50cm, what is the new width?
9. The base of an isosceles triangle is 12cm long and one of the legs is 6cm long. What is the perimeter of a similar triangle whose base is 18cm?
10. The sides of a polygon are 3, 4, 7, 9, and 11 mm long. Find the perimeter of a similar polygon whose shortest side is 10.5 mm long.
Notes: Similar Triangles
There are 3 ways you can prove triangles similar WITHOUT having to use all sides and angles.
Angle- Angle Similarity (AA~) – If two angle of one triangle are ______________ to two corresponding
angles of another triangle, then the triangles are similar
Side- Side- Side Similarity (SSS~) – If the three sides of one triangle are __________________ to the
three corresponding sides of another triangle, then the triangles are similar.
Side-Angle- Side Similarity (SAS~) – If two sides of one triangle are ____________________ to two
corresponding sides of another triangle and their included angles are ________________, then the triangles
are similar.
Examples: Determine if the triangles are similar. If so, tell why and write the similarity statement and similarity ratio.
Similar : Y or N Why:_________ Similar : Y or N Why:_________