Triangle

Properties

Part A

Table of Contents

DAY 1: (Ch. 5-1) SWBAT: Solve Problems involving the Bisectors of Triangles Pgs: 1-7 HW: Pg: 8 #1-7, 9-11, 12-17

DAY 2: (Ch. 5-2) SWBAT: Solve Problems involving the Concurrent Bisectors of Triangles

Pgs: 9-14

HW: Pgs: 15-16 #1-6, 10, 12-15, 19, 22-32

DAY 3: (5-3) SWBAT: Solve Problems involving Medians and Altitudes of Triangles Pgs: 17-22

HW: Pgs: 23-24 #1-7, 12-16, 21-32, 41-43

DAY 4: (5-4) SWBAT: Solve Problems involving the Midsegments of Triangles

Pgs: 25-29

HW: Pg: 30

DAY 5: (Review) SWBAT: Review Sections 5.1 thru 5.4

Pgs: 31-35

HW: Finish this section for homework

Day 6 – QUIZ

DAY 6: (5-5) SWBAT: Solve Problems involving Angle Relationships and Inequalities in Triangles.

Pgs: 36-39

HW: Pgs: 40-41 #4-7, 9-10, 12-14, 18-23, 26-28, 34-35, 42-52(evens)

DAY 7: (Review) SWBAT: Review Sections 5.4 thru 5.5

Pgs: 42-48

HW: Finish this section for homework

Day 8 – QUIZ

DAY 8: (Overall Review) SWBAT: Review Sections 5.1 thru 5.5

Pgs: 49-54

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Day 1 - Bisectors of Triangles

Definition of Perpendicular Bisector - A line that is perpendicular to and bisects

another segment.

2

Perpendicular Bisector Theorem

• If a point is on the perpendicular bisector of a segment, then it is

equidistant from the endpoints of the segment.

If then

Example 1:

Find AB.

Example 2:

Find WZ.

Example 3:

Find RT.

3

You Try It! Each Figure shows a triangle with one of its perpendicular bisectors.

4.

5.

6.

4

You Try It!

Angle Bisector Theorem

• If a point is on the bisector of an angle, then it is equidistant from

the two sides of the angle.

If

Converse of the Angle Bisector Theorem If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle.

5

Example 8:

Example 9:

Example 10:

11.

13.

12.

6

SUMMARY

7

Challenge

Exit Ticket

2.

8

Day 1 – HW

9

Day 2 – Concurrent Bisectors of Triangles

Warm - Up

Write the equation of the perpendicular bisector of the segments below with the given points.

X (-7, 5) Y (-1, -1)

10

You Try!

Use the figure for Exercise 5-8. , and are perpendicular bisectors of

ABC. Find each length.

5. AG = ______________

6. DB = ______________

7. AF = ______________

8. GB = ______________

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9.

12

10.

Vocabulary Recap

13

SUMMARY

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Challenge

Exit Ticket

1.

2.

15

Day 2 – HW

16

17

Day 3 – Medians and Altitudes of Triangles

Warm – Up

Ex 1: Find AB if DB = 14.1 Ex 2: Find AD if AB = 40.8

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Ex 3: K is the centroid of ABC. Find AH if KH = 6

Ex 4: L is the centroid of DEF. Find DL if DI = 21

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Ex 5: You Try It!

Ex 6: ALGEBRA

Ex 7: You Try It!

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CENTROID AND COORDINATE GEOMETRY

Ex 8: Find the centroid of ∆ABC.

Ex 9: You Try It!

Find the coordinates of the centroid of the triangle below.

An altitude of a triangle is a perpendicular segment from a vertex to the line containing the

opposite side.

Every triangle has three altitudes. An altitude can be inside, outside, or on the triangle.

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10. Where is the orthocenter located for various types of triangles?

a. For an acute triangle? b. For a right triangle? c. For an obtuse triangle?

____________ _____ ___ ________

Summary

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Challenge

Exit Ticket

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Day 3 – HW

24

25

Day 4 – Midsegments of Triangles

Warm - Up

26

27

9.

10.

11.

12

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Practice

4. Find the value of n.

Find the mAMN.

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SUMMARY

Challenge: Mark the triangles with the given information to prove the triangles congruent.

Identify the method that proves the triangles congruent.

Exit Ticket

30

Day 4 - Homework

11. Find the value of n. 12. Find the value of n.

31

Day 5 – Review: Sections 5-1 to 5-4

Warm – Up: Complete the table below.

1) The incenter of a triangle is the intersection of the ________________.

2)

3) The centroid of a triangle is the intersection of the ________________.

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4) The orthocenter of a triangle is the intersection of the ________________.

5) The incenter and centoid of a triangle are always ________________ a triangle.

6. Match the pictures with the appropriate line segments.

Perpendicular Bisectors Angle Bisectors Altitudes Median

a. b. c. d.

7. Match the pictures with the appropriate points of concurrency.

Circumcenter Incenter Centroid Orthocenter

a. b. c. d.

8.

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9.

10. Find

11.

12. Give the coordinates of the centroid of a triangle with the given vertices: M (–1, –2), N (3, –3), and P (1, -1)

Centroid _____________

13.

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14. Use the diagram below to find FG.

15. Write an equation in slope-intercept form for the perpendicular bisector of the segment with

endpoints P(3, 1) and Q(5, 5).

16.

17.

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36

Day 6 – Inequalities in Triangles

Warm – Up

Objective 1: Angle – Side – Relationships in Triangles

Example 1:

Write the angles in order from smallest to largest.

Example 2:

Write the sides in order from shortest to longest.

37

You Try It!

Example 3:

Example 4:

Objective 2: Triangle Inequality Theorem

Example 5:

You Try It!

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Example 6:

The lengths of two sides of a triangle are 8 inches and 13 inches. Find the range of possible lengths for the

third side.

You Try It!

The lengths of two sides of a triangle are 22 inches and 17 inches. Find the range of possible lengths for

the third side.

You Try It!

CHALLENGE

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SUMMARY

Exit Ticket

40

Day 6 – HW

41

42

Day 7 – REVIEW: 5-4 to 5-5

Midsegments of Triangles and Trapezoids

1. Dfd 2.

3.

4.

6.

43

7.

8.

9.

10.

11.

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12.

13.

14.

15.

16.

17.

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Objective 1: Angle – Side – Relationships in Triangles

1. In ∆PQR, PQ = 5, QR = 14, and PR = 11. What is the smallest angle?

2. In ∆XYZ, XY = 5, YZ = 7, and XZ = 8. What is the smallest angle?

3. In ∆ABC, AB = 3, BC = 4, and AC = 5. What is the largest angle?

4. In ∆ABC, and what is the shortest side of ∆ABC?

5. In ∆DEF, and what is the shortest side of ∆DEF?

6. In ∆PRS, and what is the longest side of ∆PRS?

46

7. In ∆AEM, name:

a) the shortest side

b) the longest side

8. In ∆NXS, name:

a) the shortest side

b) the longest side

9. In ∆DYC, name:

a) the shortest side

b) the longest side

10. In ∆ZPA, name:

c) the shortest side

d) the longest side

11. In ∆YES, name:

e) the shortest side

f) the longest side

12. In ∆FCX, name:

g) the shortest side

h) the longest side

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Objective 2: Triangle Inequality Theorem

13.

14.

15. In ∆PQR, PQ = 3, and QR = 9. Find all possible values of

16. In ∆PQR, PQ = 5, and QR = 7. Find all possible values of

22.

23.

24.

25.

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26

27

28

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Day 8 – Overall Review

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51

15. Write the equation of the line containing the perpendicular bisector to EF given E (4, 8) and F (-2, 6).

Write you answer in point-slope and slope-intercept form.

52

18.

19.

20.

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21. Review Ch art and answer questions below.

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