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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.
Check each inequality.



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.
A. Determine whether 6, 9, 16 can be lengths of the
sides of a triangle.
A. yes
B. no
C. cannot be
determined
1.
2.
3.
A
B
C
B. Determine whether 14, 16, 27 can be lengths of the
sides of a triangle.
A. yes
B. no
C. cannot be
determined
1.
2.
3.
A
B
C
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
Determine Possible Side Lengths
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
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.
Answer: D
In ΔXYZ, XY = 6, and YZ = 9. Which measure cannot
be XZ?
A. 4
B. 9
C. 12
D. 16
1.
2.
3.
4.
A
B
C
D
Prove Theorem 5.12
Given:
Prove:
Line
through point J
Point K lies on t.
KJ < KH
Prove Theorem 5.12
Proof:
Statements
1.
2.
are right angles.
3.
4.
5.
6.
7.
Reasons
1. Given
2. Perpendicular lines form right
angles.
3. All right angles are congruent.
4. Definition of congruent angles
5. Exterior Angle Inequality Theorem
6. Substitution
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.
Choose the correct reason to complete the following
proof.
Given:
is an altitude in ΔABC.
Prove: AB > AD
Proof:
Statements
1.
is an altitude
in ΔABC.
2.
3.
are right angles.
4.
Reasons
1. Given
2. Definition of altitude
3. Perpendicular lines form
right angles.
4. All right angles are congruent.
Proof:
Statements
5.
6.
7.
8.
Reasons
5. Definition of congruent angles
6. _____________
7. Substitution
8. 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.
A. Definition of inequality
B. Substitution
C. Triangle Inequality Theorem
D. Exterior Angle Inequality
Theorem
1.
2.
3.
4.
A
B
C
D