Similar Polygons
Proving Similar Triangles
Similar Triangles
Solving Proportions
Indirect Measurement
100
In similar polygons all angles are congruent, and all sides are ______________.
What is: Proportional
100
In triangles, ABC and XYZ? Two corresponding angles are congruent in each. What is the reason they are similar?
What is AA similarity?
100
In triangles ABC X is between A and B, Y is between A and C, and Z is between B and C. AX = 4, AB = 12, AY = 6 and AC =18. Are Triangles ABC and AXY similar? What is the scale factor? Must show work.
What is YES? AX/AB = AY/AC? 4/12 = 6/18 = 1/3 <-- scale factor
100

Solve the proportion for x:

4/2 = x/6

What is 12?
100

A tree outside Ellie’s building casts a 125 foot shadow. At the same time of day, Ellie casts a 5.5 foot shadow. If Ellie is 4 feet 10 inches tall, how tall is the tree?

What is 1319.18in OR 109.85ft

200
ABCDE ~ FGHIJ. AB = 9, FG = 15, HI = 25. CD = ?
What is: 15
200
In triangles ABC and XYZ, AB = 9, BC = 12, AC = 15. XY = 15, YZ = 20, XZ = 25. Are the triangles similar? Write the similarity statement and reason.
What is ABC ~ XYZ by SSS similarity
200
In triangles ABC X is between A and B, Y is between A and C, and Z is between B and C. AX = 14, XB =7, AY = 20, YC =12. Are triangles ABC and AXY similar? Must show work.
What is NO? AX / AB = AY / AC? 14 / 21 = 20 / 31? NOPE.
200
Solve the proportion for x:

2/6 = (x-3)/3

What is 4?

200

Cameron is 5 ft tall and casts a 12 ft shadow. At the same time of day, a nearby building casts a 78 ft shadow. How tall is the building?

What is 32.5ft

300
In, two polygons ABCD and EFGH: AB = 15, EF = 20, CD = 12 and GH = 18. Are the polygons similar?
What is: NO 15/20 = 3/4 but 12/18 = 2/3
300
In triangles ABC and XYZ, angle A = angle X, AB =10, XY = 24, AC = 5 and XZ = 12. Are the triangles similar, Write the similarity statement and reason.
What is ABC ~ XYZ by SAS similarity
300
In triangles ABC X is between A and B, Y is between A and C, and Z is between B and C. AX = 3 , XB = 1, and AY = 3YC Are triangles ABC and AXY similar? must show work.
What is YES? 3/1 =3YC/YC ; both = 3
300

Solve the proportion for x:

(x-3)/x = 6/4

What is -6?

300

Ryan is outside playing basketball. He is 5 ft tall and at this time of day is casting a 12 ft shadow. The basketball hoop is 10 ft tall. How long is the basketball hoop's shadow?

What is 24ft?

400
ABCD ~ EFGH. AB = x-5, CD = 10, FG =15, BC = 10x. What is the length of AB?
What is: 4
400
In triangles, ABC and XYZ? angle A = angle Z and angle C = angle Y. What is the similarity statement of the triangles and reason?
What is ABC ~ ZXY by AA similarity
400
In triangles ABC X is between A and B, Y is between A and C, and Z is between B and C. Triangle ABC ~ AXY . AX = 9, XB = 12, AY =15 What is YC?
What is 20?
400

Solve the proportion for x:

8/(x-7) = 10/(x-5)

What is 15?

400

Ben is 42in tall and standing 60in away from a mirror. The mirror is placed 180in from the base of a tree. How tall is the tree? 

What is 126in?

500
In polygons ABCD and EFGH, CD = 2x+4 , AB = 5x-2, EF = 1 and GH = 2. What is the length of CD?
What is: 6
500
In triangles ABC and XYZ, angle A = angle Z. AC = 50, AB =25, XZ =100 and XY =50. Are the triangles similar? If so, write the similarity statement and reason. If not, explain.
What is NO, They may not be similar because only one of the angles given is the included angle. It does not fit SAS similarity. Only if angle X = angle A then they are.
500
In triangles ABC X is between A and B, Y is between A and C, and Z is between B and C. AX = 7 , AY =4 and YC = 10. what is AB?
What is 24.5?
500

Solve the proportion for x:

(x-6)/3 = (x-10)/8

What is 18/5

500

Brenda is 5'5" and is standing 12ft from a mirror placed on the ground. The mirror is 120ft from the base of a building. How tall is the building?

What is 550in OR 45.83ft?

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