Five-Minute Check (over Lesson 3-4)Main Idea and VocabularyTargeted TEKSKey Concept: Pythagorean TheoremExample 1: Find the Length of a SideExample 2: Find the Length of a SideKey Concept: Converse of Pythagorean TheoremExample 3: Identify a Right Triangle

• legs• hypotenuse• Pythagorean Theorem• converse

• Use the Pythagorean Theorem.

8.7 The student uses geometry to model and describe the physical world. (C) Use pictures or models to demonstrate the Pythagorean Theorem. 8.9 The student uses indirect measurement to solve problems. (A) Use the Pythagorean Theorem to solve real-life problems.

Write an equation to find the length of the missing side of the right triangle. Then find the missing length. Round to the nearest tenth, if necessary.

Find the Length of a Side

c2 = a2 + b2Pythagorean Theorem

Answer: The equation has two solutions, 20 and –20. However, the length of a side must be positive. So, the hypotenuse is 20 inches long.

Find the Length of a Side

c2 = 122 + 162 Replace a with 12 and b with 16.

c2 = 144 + 256 Evaluate 122 and 162.

c2 = 400 Add 144 and 256.

c = 20 or –20 Simplify.

c = Definition of square root

A B

C D

0% 0%0%0%

A. A

B. B

C. C

D. D

A. 17 in.

B. 19 in.

C. 20 in.

D. 21 in.

Write an equation to find the length of the missing side of the right triangle. Then find the missing length. Round to the nearest tenth, if necessary.

The hypotenuse of a right triangle is 33 centimeters long and one of its legs is 28 centimeters. What is a, the length of the other leg?

Find the Length of a Side

c2 = a2 + b2Pythagorean Theorem332 = a2 + 282 Replace c with 33 and b

with 28.1,089 = a2 + 784 Evaluate 332 and 282.

1,089 – 784 = a2 + 784 – 784 Subtract 784 from each side.

305 = a2 Simplify.

= a Definition of square root17.5 ≈ a Use a calculator.

Answer: The length of the other leg is about 17.5 centimeters.

Find the Length of a Side

A B

C D

0% 0%0%0%

A. A

B. B

C. C

D. D

A. about 16.2 cm

B. about 18.5 cm

C. about 19.7 cm

D. about 21.4 cm

The hypotenuse of a right triangle is 26 centimeters long and one of its legs is 17 centimeters. What is a, the length of the other leg?

The measures of three sides of a triangle are 24 inches, 7 inches, and 25 inches. Determine whether the triangle is a right triangle.

Identify a Right Triangle

c2 = a2 + b2Pythagorean Theorem

252 = 72 + 242 Replace a with 7, b with 24, and c with 25.

?

?625 = 49 + 576 Evaluate 252, 72, and 242.

625 = 625 Simplify.

Answer: The triangle is a right triangle.

1 2 3

0% 0%0%1. A2. B3. C

A. It is a right triangle.

B. It is not a right triangle.

C. Not enough information to determine.

The measures of three sides of a triangle are 13 inches, 5 inches, and 12 inches. Determine whether the triangle is a right triangle.

http://www.tx.msmath3.com/

Five-Minute Check (over Lesson 3-5)Main IdeaTargeted TEKSExample 1: Use the Pythagorean Theorem to

Solve a ProblemExample 2: Test Example

• Solve problems using the Pythagorean Theorem.

8.7 The student uses geometry to model and describe the physical world. (C) Use pictures or models to demonstrate the Pythagorean Theorem. 8.9 The student uses indirect measurement to solve problems. (A) Use the Pythagorean Theorem to solve real-life problems.

RAMPS A ramp to a newly constructed building must be built according to the guidelines stated in the Americans with Disabilities Act. If the ramp is 24.1 feet long and the top of the ramp is 2 feet off the ground, how far is the bottom of the ramp from the base of the building?

Notice the problem involves a right triangle.

Use the Pythagorean Theorem.

Use the Pythagorean Theoremto Solve a Problem

Answer: The end of the ramp is about 24 feet from the base of the building.

24.12 = a2 + 22 Replace c with 24.1 and b with 2.

580.81 = a2 + 4 Evaluate 24.12 and 22.

580.81 – 4 = a2 + 4 – 4 Subtract 4 from each side.

576.81 = a2 Simplify.

24.0 ≈ a Simplify.

= a Definition of square root

Use the Pythagorean Theoremto Solve a Problem

A. A

B. B

C. C

D. D A B

C D

0% 0%0%0%

A. about 30.4 feet

B. about 31.5 feet

C. about 33.8 feet

D. about 35.1 feet

RAMPS If a truck ramp is 32 feet long and the top of the ramp is 10 feet off the ground, how far is the end of the ramp from the truck?

The cross-section of a camping tent is shown below. Find the width of the base of the tent.

A. 6 ft

B. 8 ft

C. 10 ft

D. 12 ft

Use the Pythagorean Theorem

Read the Test Item

From the diagram, you know that the tent forms two

congruent right triangles. Let a represent half the base of

the tent. Then w = 2a.

Use the Pythagorean Theorem

Solve the Test Item

c2 = a2 + b2 Write the relationship.102 = a2 + 82 c = 10 and b = 8100 = a2 + 64 Evaluate 102 and 82.

100 – 64 = a2 + 64 – 64 Subtract 64 from each side.

36 = a2 Simplify.

Use the Pythagorean Theorem.

= a Definition of square root6 = a Simplify.

Use the Pythagorean Theorem

Answer: The width of the base of the tent is 2a or (2)6 = 12 feet. Therefore, choice D is correct.

The cross-section of a camping tent is shown below. Find the width of the base of the tent.

A. 6 ft

B. 8 ft

C. 10 ft

D. 12 ft

Use the Pythagorean Theorem

A. A

B. B

C. C

D. D

A B

C D

0% 0%0%0%

A. 15 ft

B. 18 ft

C. 20 ft

D. 22 ft

This picture shows the cross-section of a roof. How long is each rafter, r?

Five-Minute Check (over Lesson 3-6)Main Ideas and VocabularyTargeted TEKSExample 1: Name an Ordered PairExample 2: Name an Ordered PairExample 3: Graphing Ordered PairsExample 4: Graphing Ordered PairsExample 5: Find Distance on the Coordinate PlaneExample 6: Use a Coordinate Plane to Solve a

Problem

• coordinate plane

• Graph rational numbers on the coordinate plane.

• origin• y-axis• x-axis• quadrants

• ordered pair• x-coordinate• abscissa• y-coordinate• ordinate

• Find the distance between two points on the coordinate plane.

8.7 The student uses geometry to model and describe the physical world. (D) Locate and name points on the coordinate plane using ordered pairs of rational numbers. 8.9 The student uses indirect measurement to solve problems. (A) Use the Pythagorean Theorem to solve real-life problems. Also addresses TEKS 8.1(C).

• Start at the origin.

Name the ordered pair for point A.

Name an Ordered Pair

• Move right to find the x-coordinate of point A, which is 2.

• Move up to find the y-coordinate, which is

Answer: So, the ordered pair for point A is

A. A

B. B

C. C

D. D

A B

C D

0% 0%0%0%

A.

B.

C.

D.

Name the ordered pair for point A.

• Start at the origin.

Name the ordered pair for point B.

Name an Ordered Pair

• Move down to find the y-coordinate, which is –2.

• Move left to find the x-coordinate of point B,

which is

Answer: So, the ordered pair for point B is

A. A

B. B

C. C

D. D

A B

C D

0% 0%0%0%

A.

B.

C.

D.

Name the ordered pair for point B.

• Start at the origin and move 3 units to the left. Then move up 2.75 units.

• Draw a dot and label it J(–3, 2.75).

Graph and label point J(–3, 2.75).

Graphing Ordered Pairs

Answer:

A. A

B. B

C. C

D. D A B

C D

0% 0%0%0%

Graph and label point J(–2.5, 3.5).

A.

B.

C.

D.

Graphing Ordered Pairs

Answer:

Graph and label point K

• Start at the origin and move 4 units to the right.

Then move down units.

• Draw a dot and label it

K

A. A

B. B

C. C

D. D A B

C D

0% 0%0%0%

Graph and label point K

A.

B.

C.

D.

Let c = the distance between the two points, a = 5, and b = 5.

Graph the ordered pairs (0, –6) and (5, –1). Then find the distance between the points.

Find Distance in the Coordinate Plane

Find Distance in the Coordinate Plane

Answer: The points are about 7.1 units apart.

c2 = a2 + b2 Pythagorean Theorem

c ≈ 7.1 Simplify.

= Definition of square root

c2 = 52 + 52 Replace a with 5 and b with 5.

c2 = 50 52 + 52 = 50

A. A

B. B

C. C

D. D A B

C D

0% 0%0%0%

A. about 3.1 units

B. about 3.6 units

C. about 3.9 units

D. about 4.2 units

Graph the ordered pairs (0, –3) and (2, –6). Then find the distance between the points.

TRAVEL Melissa lives in Chicago, Illinois. A unit on the grid of her map shown below is 0.08 mile. Find the distance between McCormickville at (–2, –1) and Lake Shore Park at (2, 2).

Let c = the distance between McCormickville and Lake Shore Park. Then a = 3 and b = 4.

Use a Coordinate Plane to Solve a Problem

Answer: Since each unit equals 0.08 mile, the distance is 0.08 5 or 0.4 mile.

c2 = a2 + b2 Pythagorean Theorem

c = 5 Simplify.

c2 = 32 + 42 Replace a with 3 and b with 4.

c2 = 25 32 + 42 = 25

= Definition of square root

The distance between McCormickville and Lake Shore Park is 5 units on the map.

Use a Coordinate Plane to Solve a Problem

A. A

B. B

C. C

D. D

A B

C D

0% 0%0%0%

A. about 0.1 mileB. about 0.2 mileC. about 0.3 mileD. about 0.4 mile

TRAVEL Sato lives in Chicago. A unit on the grid of his map shown below is 0.08 mile. Find the distance between Shantytown at (2, –1) and the intersection of N. Wabash Ave. and E. Superior St. at (–3, 1).