Ratios & Proportions
What is a ratio?
A comparison of two quantities
What do we call the numbers in a proportion that are across from each other in a fraction?
Extremes & Means
What is a scale drawing?
A drawing that compares each length to the actual length.
What does it mean for two polygons to be similar?
They have the same shape but not necessarily the same size.
What does the Side-Splitter Theorem say?
If a line parallel to one side of a triangle intersects the other two sides, it divides them proportionally.
The ratio of boys to girls in a class is 14:18. What is the ratio of girls to boys?
18:14 or 9:7
State the Cross product Property of proportions
if a/b = c/d, then ad=bc
A model car is 4 in. long. The actual car is 15 ft. What is the ratio of model to actual in inches?
4:180 (simplified to 2:90 or 1:45).
What is the symbol for similarity?
~
If DE || AC in triangle ABC, how do we write a proportion?
BD/DA = BE/EC.
Solve for x: 7/x = 3/6
X=14
What is the Reciprocal property of proportions?
if a/b = c/d, then b/a = d/c
You are making a map with a scale of 1 in. = 35 miles. How many inches apart would two cities be if they are 175 miles apart?
5 inches.
What does the Angle-Angle (AA) Similarity Theorem state?
If two angles of one triangle are equal to two angles of another triangle, the triangles are similar.
What does the Triangle Angle Bisector Theorem state?
A bisector of an angle divides the opposite side into segments proportional to the other two sides.
What is a proportion?
An equation that equates two ratios.
Solve for x: 4/5 = x/10
X=8
A building is 50 ft tall, and its scale model is 10 inches tall. What is the scale?
1 in = 5 ft.
The sides of one triangle are 12, 14, and 16. The sides of another are 18, 21, and 24. Are they similar? Why?
Yes, because their sides have the same ratio (2:3). This follows the Side-Side-Side (SSS) Similarity Theorem.
If a ray bisects an angle in a triangle and divides the opposite side into segments 3 and 6, what is the proportion?
3/6 = other side proportion.