Section 7-1, Ratios and Proportions
Ratio:
Ratios can be written in three ways:
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Because a ratio is a quotient (fraction), its denominator CANNOT be _________. Ratios are expressed in
_______________ form.
Example 1: A baseball player’s batting average is the ratio of the number of base hits to the number of at-bats, not including walks. If a player had 521 official at-bats and 181 hits, find his batting average.
Example 2: In Chad’s high school, there are 190 teachers and 2650 students. What is the approximate student-teacher ratio at his school?
Example 3: The number of students that participate in sports at a particular high school is 520. The total number of students at the school is 1850. Find the athlete-to-student ratio at this school.

Extended Ratios:
The ratio a:b:c means that the ratio of the ________ two quantities is ________, the ratio of the _______ two quantities is _________, and the ratio of the _______ and ________ quantities is ____________.
Example 4: The ratios of the angles in ∆ABC is 3:5:7. Find the measures of the angles.
Example 5: In a triangle, the ratio of the measures of the sides is 3:3:8 and the perimeter is 392. Find the length of each side of the triangle.
Example 6: The ratio of the angles in a quadrilateral is 2:4:6:3. Find the measures of the angles in the quadrilateral.
Example 7: The perimeter of a rectangle is 98 feet. The ratio of its length to its width is 7:3. Find the area of the rectangle.
Example 8: Solve each proportion using cross products.

ASSIGNMENT
Day 1: Skills and Practice 7-1
Due on Tuesday, Dec. 1
7-2, Similar Polygons
Review
Congruent 
Vocabulary
Similar:
Symbol 
Similarity Ratio:
Polygons are similar if:
Practice with Corresponding Parts
If ∆ABC~∆RST, list all pairs of congruent angles and write a proportion that relates the corresponding sides.

Practice with Corresponding Parts
Scale Factors: also called:
Practice Determining Similarity
Are the two triangles similar?
Step 1: Make sure the angles are congruent.
Step 2: Decide how to compare the sides.
Ex…small to big, or big to small
Step 3: Create ratios from each pair of corresponding sides. Remember to simplify.
If the ratios are the same (when they are simplified), then the triangles are similar.
Practice Determining Similarity
Taylor is designing a new menu for the restaurant where she works. Determine whether the size for the menu is similar to the original menu. If so, write the similarity statement and scale factor. Explain your reasoning.
Practice Determining Similarity

Practice Finding Variables
These polygons are similar. Find the values of the variables.
Finding Perimeters Using Similarity
If LMNOP~VWXYZ, find the perimeter of each polygon.
Finding Perimeter Using Similarity
If ∆WZY is similar to ∆SRT and ST=6 and WX=5, and the perimeter of ∆SRT=15, find the perimeter of ∆WZX.
Two similar rectangles have a scale factor of 2:4. The perimeter of the larger rectangle is 80 meters. Find the perimeter of the smaller rectangle.

ASSIGNMENT
Day 1: Worksheet 7-2
Due on Wednesday, December 2
7-3, Similar Triangles
Review
Triangle Congruence Theorems cannot prove congruency by:
Triangle Similarity

Practice Identifying Similarity Properties (Theorems)
Practice Identifying Similarity Properties and Finding Missing Variables
State why the triangles are similar, then find the missing variable.
Practice Finding Missing Variables

Practice with Shadow Problems
In sunlight, a cactus casts a 9-foot shadow. At the same time, a 6-foot tall person casts a 4-foot shadow. Use similar triangles to find the height of the cactus.
Practice with Shadow Problems
Summary
Tori wanted to measure the height of the Sears Tower in Chicago. She used a 12 foot light pole and measured its shadow at 1pm. The length of the shadow was 2 feet. Then he measured the length of the Sears Tower’s shadow, and it was
242 feet at the same time. What is the height of the Sears Tower?
Sears Tower

ASSIGNMENT
Day 1: Worksheet 7-3, Day 1
Due on Friday, Dec. 4
Day 2: Worksheet 7-3, Day 2
Due on Monday, Dec. 7
7-4 and 7-5, Parts of Similar Triangles
Side Splitter Theorem: If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.
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S B
U N
Practice with Side Splitter Theorem
Proportional Parts of Parallel Lines: If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional. h j f g
Practice with Proportional Parts of Parallel Lines

Triangle-Angle Bisector Theorem: If a ray bisects an angle of a triangle, then it divides the opposite sides into two segments that are proportional to the other two sides of the triangle.
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A
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C
Practice with Triangle-Angle Bisector Theorem
Practice with Triangle-Angle Bisector Theorem and Parallel Lines (difficult)
Special Segments in Similar Triangles

Practice with Special Segments
Congruent Parts of Parallel Lines
Practice with Congruent Parts of Parallel Lines
ASSIGNMENT
Day 1: 7-4 and 7-5, Day 1
Due on Tuesday, Dec. 8
Day 2: 7-4 and 7-5, Day 2
Due on Wednesday, Dec. 9