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.

• perpendicular bisector

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

B. Find WYZ.

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.

• median

• altitude

• 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.