Lesson 6 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.

Set

2.

Using the right triangle with altitude drawn to the hypotenuse, prove the Pythagorean theorem, $a^{2} + b^{2} = c^{2}$ .

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

3.

4.

5.

6.

Go

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

7.

8.

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

9.

a.

When a line is drawn parallel to $\overset{―}{A C}$ through point $D$ , where will it intersect $\overset{―}{B C}$ ?

b.

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

10.

a.

When a line is drawn parallel to $\overset{―}{B C}$ through point $D$ , where will it intersect $\overset{―}{A C}$ ?

b.

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

11.

Place point $C$ on the segment to split it into two segments with lengths that are a ratio of $1 : 2$ .

12.

Place point $C$ on the segment to split it into two segments with lengths that are a ratio of $3 : 1$ .

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	$1$	$2$	$3$	$4$
Value	$7$			$22$

Explicit function rule:

14.

A Geometric Sequence

Term	$1$	$2$	$3$	$4$
Value	$7$			$56$

Explicit function rule:

15.

An Arithmetic Sequence

Term	$5$	$6$	$7$	$8$
Value	$10$			$43$

Explicit function rule:

16.

A Geometric Sequence

Term	$7$	$8$	$9$	$10$
Value	$3$			$24$

Explicit function rule: