lesson 4 menu 1.write the assumption you would make to start an indirect proof of the statement:...
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1. Write the assumption you would make to start an indirect proof of the statement: ΔABC is congruent to ΔDEF.
2. Write the assumption you would make to start an indirect proof of the statement: RS is an angle bisector.
3. Write the assumption you would make to start an indirect proof of the statement: X is a right angle.
4. Write the assumption you would make to start an indirect proof of the statement: If 4x – 3 9, then x 3.
5. Write the assumption you would make to start an indirect proof of the statement: ΔMNO is an equilateral triangle.
• Apply the Triangle Inequality Theorem.
• Determine the shortest distance between a point and a line.
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.
1. A
2. B
3. C
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
B. Determine whether 14, 16, 27 can be lengths of the sides of a triangle.
A. yes
B. no
C. cannot be determined
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
1. A
2. B
3. C
4. D
A. 4
B. 9
C. 12
D. 16
In ΔXYZ, XY = 6, and YZ = 9. Which measure cannot be XZ?
Prove Theorem 5.12
Prove: KJ < KH
Given: Line through point JPoint K lies on t.
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
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
A. Definition of inequality
B. Substitution
C. Triangle Inequality Theorem
D. Exterior Angle Inequality Theorem
