A Similar Triangles Conjecture

Name______Hour______

In the triangles to the right,

 What is the measure of and why?

Measure the sides and compare the ratios of corresponding side lengths.

 Is ?

 Is ? Why or why not?

Now, draw your own with different side lengths between 2cm and 5cm long.

Construct a 2nd triangle, , above as well, but with different side lengths of . Make this triangle not congruent to but with and (use a protractor and ruler to help you) Are your two triangles similar? Explain. Similarity Practice 2 Name______Hour______Ready 1. How can you determine if two polygons are similar?

Explain if each statement is true or false. Explain your reasoning. 2. All squares are similar.

3. If an acute angle of a right triangle is congruent to an acute angle of a second right triangle, then the triangles are similar.

4. All isosceles triangles are similar.

For #5-7, (See figure on right 5. Find 6. Find AQ. 7. Find AB.

Set For problems #8-11, For each problem, sketch and label the given angles or sides for Then solve for t. 8.

10.

11. 12. Alicia and Jason were writing proportions for similar triangles shown at the right.

Who is correct? Explain your reasoning.

13. Identify the similar triangles (write a similarity statement). Find x and the measures of the sides AB and DE.

Go! 15. To make concrete for the footings of her new deck, Marie mixes cement and sand in a ratio of 2 bags cement to 3 bags of sand. How many bags of sand will she need if she uses 32 bags of cement?

16. A 212-pound person weighs about 34 pounds on the moon. About how much will a 130-pound person weight on the moon?

17. A baker’s recipe calls for 6 cups of flour for every 2 cups of milk. If the baker uses 9 cups of flour, how many cups of milk will he need?

18. A machine worker can produce 75 auto parts in 1.5 hours. How many auto parts can the worker produce in 5 hours?

19. A survey shows that four out of every seven students watches TV more than three hours per day. If there are 560 seniors in a high school, how many would you expect to watch more than three hours of TV every day?

20. The advertisement for a scale model of a classic automobile gives the scale of the model as 1 to 24. The model is inches long. What is the actual length of the automobile?