Similarity
In similar triangles, corresponding angles are...
Congruent
In two similar triangles, the sides of the smaller triangle are x and 5, which correspond to sides of length 6 and 10, respectively, in the larger triangle. What is the value of x?
3
A model train is constructed using the scale 1 inch : 5 feet. If the length of the model train is 8 inches, what is the actual length of the train in feet?
40 feet
This similarity theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar
AA similarity
10x MULTIPLIER!: What did Mr. Dolan dress up as for Halloween?
A holy cow
In similar triangles, corresponding sides are...
Proportional
In two similar triangles, the sides of the smaller triangle are x and 6, which correspond to sides of length 10 and 12 in the larger triangle. What is the value of x?
5
A room on an architectural blueprint is 5 inches wide and 8 inches long. The actual room in the building is 25 feet wide. What is the actual length of the room?
40 feet
This similarity theorem states that if two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent, then the triangles are similar.
SAS similarity
What casa is Mr. Dolan in?
Casa Kateri
This number tells you how much a figure has been enlarged (made larger) or reduced (made smaller)
Scale Factor
In two similar triangles, the sides of the smaller triangle are x and 12, which correspond to sides of length 14 and 21 in the larger triangle. What is the value of x?
8
A scale model of a suspension bridge uses the scale 3 inches : 14 feet. If the length of the model bridge is 15 inches, what is the actual length of the bridge in feet?
70 feet
This similarity theorem states that two triangles are similar if the lengths of all three pairs of their corresponding sides are proportional (in the same ratio)
SSS similarity
July
What does it mean for corresponding sides to be proportional?
Every corresponding side of one shape has been scaled up or down by the exact same number compared to the corresponding side of the other shape
In two similar quadrilaterals, a side of length x corresponds to a side of length 15, and a side of length 14 corresponds to a side of length 35. What is the value of x?
6
A map of a county uses the scale 4 centimeters : 15 miles. If the actual distance between two towns is 105 miles, what is the distance between the two towns on the map in centimeters?
28 centimeters
Triangle 1 has interior angles measuring 40 degrees and 60 degrees. Triangle 2 has interior angles measuring 60 degrees and 80 degrees. Are these two triangles similar? Answer yes or no.
Yes
What is Mr. Dolan's favorite holiday?
Christmas
What is the difference between similarity and congruence?
Similar figures share the same shape, but not necessarily the same size (congruent figures share both)
In two similar triangles, a pair of corresponding sides have lengths x and x + 4. If another pair of corresponding sides has lengths of 9 and 15, what is the value of x?
6
A designer draws a floor plan for a rectangular patio using the scale 2 centimeters : 9 feet. On the plan, the patio is 6 centimeters long and 4 centimeters wide. What is the actual area of the patio in square feet? Include units in your answer.
486 ft²
Triangle A has sides measuring 4, 6, and 8. Triangle B has corresponding sides measuring 12, 18, and 24.
Identify both the similarity theorem that proves these two triangles are similar and the scale factor from the smaller triangle to the bigger triangle.
SSS, 3
How many mentees does Mr. Dolan have?
16