Lesson 7 Pythagoras by Proportions Practice Understanding

Ready

1.

Determine which of the triangles below are similar and which are congruent. Justify your conclusions. Give your reasoning for the triangles you pick to be similar and congruent.

Triangles A, B, C, D, E, F, G, H with various angles marked congruent.

Set

2.

Using the right triangle with altitude drawn to the hypotenuse, prove the Pythagorean theorem, .

Triangle ABC with altitude CP.

Find the missing values for each right triangle including the length of the altitude.

3.

Triangle with sides 5,12,x and altitude y.

4.

Triangle with sides b,5, 8 and altitude a.

5.

Triangle ABC with sides b, a, 10 and altitude CD labeled n.

6.

Triangle ABC with sides c, 8, 15 and altitude CD labeled n.

Go

In each problem, find the missing values using the similar triangles, parallel lines, and proportional relationships. Write a proportion and solve.

7.

Triangle with interior line segment parallel to the base.

8.

Triangle with interior line segment parallel to the base.

For questions 9–12, use the grids provided to determine the indicated segment measures and the proportions.

9.

Triangle ABC; A(-3,-3), B(-3,3) C(6,3) with point D(-3,-1). x–5–5–5555y000AAABBBCCCDDD

a.

When a line is drawn parallel to through point , where will it intersect ?

b.

What is the ratio of the lengths of the two segments created by point ?

10.

triangle ABC on a coordinate plane with point D on line AB x–5–5–5555y555000AAABBBCCCDDD

a.

When a line is drawn parallel to through point , where will it intersect ?

b.

What is the ratio of the lengths of the two segments created by point ?

11.

Place point on the segment to split it into two segments with lengths that are a ratio of .

Line segment AB with A(-5,-3) and B(7,3). x–5–5–5555y–5–5–5555000

12.

Place point on the segment to split it into two segments with lengths that are a ratio of .

Line segment AB with A(-5,-3) and B(4,8) x–5–5–5555y–5–5–5555000

Analyze each table closely and determine the missing values based on the given information and values in the table. Create an explicit function rule for the sequence.

13.

An Arithmetic Sequence

Term

Value

Explicit function rule:

14.

A Geometric Sequence

Term

Value

Explicit function rule:

15.

An Arithmetic Sequence

Term

Value

Explicit function rule:

16.

A Geometric Sequence

Term

Value

Explicit function rule: