Five-Minute Check (over Lesson 5-3)

Main Ideas

California Standards

Theorem 5.11: Triangle Inequality Theorem

Example 1: Identify Sides of a Triangle

Example 2: Standards Example: Determine Possible Side Length

Theorem 5.12

Example 3: Prove Theorem 5.12

Corollary 5.1

Do Now

Do Now

• Apply the Triangle Inequality Theorem.

• Determine the shortest distance between a point and a line.

http://www.geogebra.org/en/upload/files/english/dtravis/triangle_inequality.html

http://www.geogebratube.org/student/m130

http://www.geogebra.org/en/upload/files/english/nebsary/TriangleInequality/TriangleInequalityFinal.html

http://www.ca.geometryonline.com/

Identify Sides of a Triangle

Answer: Because the sum of two measures is not greater than the length of the third side, the sides cannot form a triangle.

Identify Sides of a Triangle

B. Determine whether the measures 6.8, 7.2, and 5.1 can be lengths of the sides of a triangle.

Answer: All of the inequalities are true, so 6.8, 7.2, and 5.1 can be the lengths of the sides of a triangle.

Check each inequality.

Determine Possible Side Lengths

In ΔPQR, PQ = 7.2 and QR = 5.2. Which measure cannot be PR?

A 7

B 9

C 11

D 13

Read the Item

You need to determine which value is not valid.

Solve the Item

Solve each inequality to determine the range of values for PR.

Determine Possible Side Lengths

Graph the inequalities on the same number line.

The range of values that fit all three inequalities is

Determine Possible Side Lengths

Answer: D

Examine the answer choices. The only value that does not satisfy the compound inequality is 13 since 13 is greater than 12.4. Thus, the answer is choice D.

Determine Possible Side Lengths

http://www.ca.geometryonline.com/

Prove Theorem 5.12

Prove: KJ < KH

Given: Line through point JPoint K lies on t.

HE EG

K

H

Prove Theorem 5.12

1. 1. Given

are right angles.2. 2. Perpendicular lines form right

angles.3. 3. All right angles are congruent.4. 4. Definition of congruent angles

7. 7. If an angle of a triangle is greater than a second angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.

Proof:Statements Reasons

6. 6. Substitution5. 5. Exterior Angle Inequality Theorem

http://www.ca.geometryonline.com/

http://www.ca.geometryonline.com/

1. A

2. B

3. C

A B C

0% 0%0%

A. Determine whether 6, 9, 16 can be lengths of the sides of a triangle.

A. yes

B. no

C. cannot be determined

1. A

2. B

3. C

A B C

0% 0%0%

B. Determine whether 14, 16, 27 can be lengths of the sides of a triangle.

A. yes

B. no

C. cannot be determined

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 4

B. 9

C. 12

D. 16

In ΔXYZ, XY = 6, and YZ = 9. Which measure cannot be XZ?

Choose the correct reason to complete the following proof.

Prove: AB > AD

Given: is an altitude in ΔABC.

Proof:Statements

1.

2.3.

4.

Reasons

1. Given

2. Definition of altitude3. Perpendicular lines form

right angles.4. All right angles are congruent.

is an altitude in ΔABC.

are right angles.

Proof:Statements

5.6.7.8.

Reasons

5. Definition of congruent angles 6. _____________7. Substitution8. If an angle of a triangle is greater

than a second angle, then the side opposite the greater angle is

longer than the side opposite the lesser angle.

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. Definition of inequality

B. Substitution

C. Triangle Inequality Theorem

D. Exterior Angle Inequality Theorem