Lesson 3 Similar Triangles & Other Figures Solidify Understanding

Ready

Solve each proportion. Show your work and check your solution.

1.

2.

3.

4.

5.

6.

7.

8.

9.

Set

Provide an argument to prove each conjecture, or provide a counterexample to disprove it.

10.

All right triangles are similar.

11.

All regular polygons are similar to other regular polygons with the same number of sides.

12.

The polygons on the grid are similar.

Similar Pentagon LMNOP and smaller pentagon L'M'N'O'P'

13.

The polygons on the grid are similar.

Similar Quadrilateral GIJK with smaller quadrilateral G'I'J'K' rotated 180 degrees.

A sequence of transformations occurred to create the two similar polygons. Provide a specific set of steps that can be used to create the image from the pre-image with one, two, or three transformations.

14.

Triangle ABC with A pointing downwards and Triangle AB"C" with point A facing to the left.

15.

Hexagon EHILKM and Hexagon E'H'I'L'K'M'

16.

Larger Triangle BCD and smaller triangle B"C"D"

17.

Quadrilateral ABCD with A pointing to the right. Quadrilateral AB"C"D" with A pointing upwards.

18.

One definition of similar triangles is based on transformations. However, there are other criteria for determining whether or not triangles are similar. What are these other criteria?

19.

Determine whether or not the pairs of triangles are similar and explain why.

a.

Larger triangle with two angles marked congruent and smaller triangle with two angles marked congruent.

b.

Smaller triangle with sides 3,4,8 and larger triangle with sides 9,12,22

c.

Larger triangle with two angles marked congruent and smaller triangle with two angles marked congruent.

Go

For each pair of similar polygons, give three ratios that would be equivalent.

20.

Smaller Triangle with sides 3,a,1.5 and larger triangle with sides c,5,3

21.

Smaller pentagon with sides 2,6,x,4,y and larger pentagon with sides 4,a,8,n,10

22.

Two triangles that share the longer side, one triangle with sides d and x the other with sides x and 21.

23.

Smaller triangle with sides 3,4,5 and larger triangle with sides 6,8,10