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Five-Minute Check (over Chapter 4)
Then/Now
New Vocabulary
Theorems: Perpendicular Bisectors
Example 1: Use the Perpendicular Bisector Theorems
Theorem 5.3: Circumcenter Theorem
Proof: Circumcenter Theorem
Example 2: Real-World Example: Use the Circumcenter Theorem
Theorems: Angle Bisectors
Example 3: Use the Angle Bisector Theorems
Theorem 5.6: Incenter Theorem
Example 4: Use the Incenter Theorem
Over Chapter 4
A. scalene
B. isosceles
C. equilateral
Classify the triangle.
A. A
B. B
C. C
A B C
0% 0%0%
Over Chapter 4
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 3.75
B. 6
C. 12
D. 16.5
Find x if mA = 10x + 15, mB = 8x – 18, and mC = 12x + 3.
Over Chapter 4
A. R V, S W, T U
B. R W, S U, T V
C. R U, S V, T W
D. R U, S W, T V
Name the corresponding congruent sides if ΔRST ΔUVW.
A. A
B. B
C. C
A B C
0% 0%0%
Over Chapter 4
Name the corresponding congruent sides if ΔLMN ΔOPQ.
A. A
B. B
C. C
A B C
0% 0%0%
A.
B.
C.
D. ,
Over Chapter 4
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 22
B. 10.75
C. 7
D. 4.5
Find y if ΔDEF is an equilateral triangle and mF = 8y + 4.
You used segment and angle bisectors. (Lesson 1–3 and 1–4)
• Identify and use perpendicular bisectors in triangles.
• Identify and use angle bisectors in triangles.
Use the Perpendicular Bisector Theorems
A. Find the measure of BC.
Answer: 8.5
BC = AC Perpendicular Bisector Theorem
BC = 8.5 Substitution
Use the Perpendicular Bisector Theorems
B. Find the measure of XY.
Answer: 6
Use the Perpendicular Bisector Theorems
C. Find the measure of PQ.
PQ = RQ Perpendicular Bisector Theorem
3x + 1 = 5x – 3 Substitution
1 = 2x – 3 Subtract 3x from each side.
4 = 2x Add 3 to each side.
2 = x Divide each side by 2.
So, PQ = 3(2) + 1 = 7.
Answer: 7
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 4.6
B. 9.2
C. 18.4
D. 36.8
A. Find the measure of NO.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 2
B. 4
C. 8
D. 16
B. Find the measure of TU.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 8
B. 12
C. 16
D. 20
C. Find the measure of EH.
Use the Angle Bisector Theorems
A. Find DB.
Answer: DB = 5
DB = DC Angle Bisector Theorem
DB = 5 Substitution
Use the Angle Bisector Theorems
Answer: mWYZ = 28
WYZ XYZ Definition of angle bisector
mWYZ = mXYZ Definition of congruent angles
mWYZ = 28 Substitution
Use the Angle Bisector Theorems
C. Find QS.
Answer: So, QS = 4(3) – 1 or 11.
QS = SR Angle Bisector Theorem
4x – 1 = 3x + 2 Substitution
x – 1 = 2 Subtract 3x from each side.
x = 3 Add 1 to each side.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 22
B. 5.5
C. 11
D. 2.25
A. Find the measure of SR.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 28
B. 30
C. 15
D. 30
B. Find the measure of HFI.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 7
B. 14
C. 19
D. 25
C. Find the measure of UV.
• Altitude:Altitude: (of a triangle) is a segment from a vertex to the line containing the opposite side and perpendicular to the line containing that side.
• Median:Median: (of a triangle) is a segment with endpoints being a vertex of a triangle and the midpoint of the opposite side.