Ratios and Proportions
A number that ends in 5 or 0, will always be divisible by ________.
5
Polygons are similar if corresponding angles are _____________ and corresponding sides are __________________.
congruent
proportional
Using AA similarity, you can prove that 2 triangles are congruent if you have 2 pairs of corresponding angles that are _________.
Congruent
You can use SSS similarity to prove 2 triangles are congruent if all corresponding sides are ___________.
Proportional
An angle bisector in a triangle separates the opposite sides into two segments that are proportional to the lengths of the other two sides.
What is the above theorem called?
A. Triangle Proportionality Theorem
B. Triangle Angle Bisector Theorem
B. Triangle Angle Bisector Theorem
What is the simplest form of the ratio 39:57
13:19
The ratio of the corresponding sides of a similar polygon is called the ________ __________.
Scale Factor
True or False. If 2 pairs of corresponding sides are proportional and any corresponding angles are congruent between 2 triangles, then you can use SAS similarity to prove that the triangles are similar.
FALSE - The congruent angles have to be the included angles
If Triangle RST ~ Triangle XYZ, what side of Triangle XYZ would correspond to RT?
XZ
The Triangle Proportionality Theorem says: If a line is _______ to one side of a triangle and intersects the other 2 sides, then it divides the sides into segments of proportional lengths.
What word goes in the blank?
Parallel
What is the greatest common factor (GCF) of 17 and 85?
17
Look at Picture 1. What is the scale factor of Figure B to Figure A in simplest form?
2:5
True or False. Look at Picture 4. If that proportion represents the corresponding sides of 2 triangles, you could prove the 2 triangles are similar using SSS.
False
Look at Picture 7. Determine how (if possible) the triangles can be proved similar.
A. AA~
B. SSS~
C. SAS~
D. Not Similar
A. AA~
Look at Picture 10. Using the Triangle Proportionality Theorem, what proportion could I use to solve for x?
15 / 8=x / 10
Multiple Correct Answers
If the ratio of the angles in a triangle is 3:5:7, how many degrees would the largest angle be?
84 degrees
Look at Picture 2. If Triangle ABC ~ Triangle DEF, what proportion could I use to solve for X?
56 / 42 = 6x-14 / 2x+22
(Multiple Correct Answers)
Look at Picture 5. Determine how (if possible) the triangles can be proved similar.
A. AA~
B. SSS~
C. SAS~
D. Not Similar
C. SAS~
Look at Picture 8. Determine how (if possible) the triangles can be proved similar.
A. AA~
B. SSS~
C. SAS~
D. Not Similar
C. SAS~
Look at Picture 11. If LM bisects angle JKL, using the Triangle Angle Bisector Theorem, what proportion could I use to solve for x?
4 / x = 8 / x+3 or x / 4 = x+3 / 8
If the ratio of the sides of a triangle are 2:3:5 and the perimeter of the triangle is 150 inches, how long would the shortest side be?
30 inches
Look at Picture 3. If Triangle GHJ ~ Triangle LMK, with a scale factor of 5:6, what proportion could I use to find the perimeter of Triangle GHJ?
5 / 6=x / 21
(Multiple Correct Answers)
Look at Picture 6. Determine how (if possible) the triangles can be proved similar.
A. AA~
B. SSS~
C. SAS~
D. Not Similar
B. SSS~
Look at Picture 9. Determine how (if possible) the triangles can be proved similar.
A. AA~
B. SSS~
C. SAS~
D. Not Similar
D. Not Similar
Look at Picture 12. If VT bisects angle STU, Using the Triangle Angle Bisector Theorem, what proportion could I use to solve for x?
12 / 32 = 16 / 3x+2 or 32 /12 = 3x+2 / 16