Congruent Triangles
True or False: All congruent triangles are also similar.
True
You have triangles ABC and XYZ and two corresponding angles are congruent in each. What is the reason they are similar?
What is AA similarity
If the scale factor of a dilation is 4/3 is it an enlargement or a reduction?
What is enlargement?
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
On a map 1 inch = 50 miles. If point A is 7.5 inches from point B on the map. How far is point A from point B in the real world?
(90 seconds)
What is 375 miles?
Which triangle congruence theorem states that if all three sides of one triangle are congruent to the corresponding sides of another triangle, then the triangles are congruent? (30 seconds)
SSS (side-side-side)
If a figure has the side lengths of 24, 16, and 20, and a similar figure has side lengths of 10, 8, and 12, what is the scale factor?
What is 1/2?
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 / 32? NOPE.
On a map 2 inches = 80 miles. If Atlanta is 400 miles from West Virginia in the real world, how far apart are they on the map?
(90 seconds)
What is 10 inches?
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, which triangle congruence theorem can be used to prove the triangles congruent? (30 seconds)
SAS (side-angle-side)
If the original figure has the coordinates A(1,2) B(4,9) C(3,2) and has a scale factor of 3, what are the dilated coordinates?
What is A'(3,6) B'(12,27) C'(9,6)?
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
A model car is 6 inches long, the real car is 15 feet long. What is the scale of the model to the real car?
(90 seconds)
What is 1inch : 2.5 feet?
What is the name of the theorem that states if two angles and a non-included side of one triangle are congruent to the corresponding angles and non-included side of another triangle, then the triangles are congruent? (30 seconds)
AAS (angle-angle-side)
You have triangles ABC and XYZ and 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
If figure A has angles of 23o, 57o, and 100o, what would be the angles of a similar figure?
The same.
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?
Two triangles are similar. The smaller triangle has a side of 5 and a height of 8. The larger one has a corresponding side that measures 20. What is the height of the larger one?
(90 seconds)
What is 32?
Which triangle congruence theorem states that if two angles and the included side of one triangle are congruent to the corresponding angles and included side of another triangle, then the triangles are congruent? (30 seconds)
ASA (angle-side-angle)
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.
What are the side lengths of the dilated figure of ABC with a scale factor of 3/4?
AC=24
CB=12
BA=8
A'C'=18
C'B'=9
B'A'=6
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?
You want to determine the height of a flagpole. You have a friend place a small mirror on the ground so that you can see the reflection of the top of the flagpole. Your friend then measures from you to the mirror and finds that it is 3 feet. The distance from the mirror to the flagpole is 15 feet. The angle from the mirror to your eyes is about 15 degrees, and the angle from the top of the flagpole to the mirror is also about 15 degrees. If your eyes are 5 feet above the ground, how high is the flagpole?
(90 seconds)
What is 25 ft?