Triangle Properties Part A · DAY 2: (Ch. 5-2) SWBAT: Solve Problems involving the Concurrent Lines...

Triangle

Properties

Part A

Table of Contents

DAY 1: (Ch. 5-1/5-3) SWBAT: Solve Problems involving the Bisectors and Medians of Triangles Pgs: 1-9 HW: Pgs: #9-11

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

Pgs: 12-16

HW: Pgs: #17-19

DAY 3: (5-4) SWBAT: Solve Problems involving the Midsegments of Triangles

Pgs: 20-24

HW: Page: 25

Day 4 – QUIZ

SWBAT: Review Sections 5.1 thru 5.4

Pgs: 26-30

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

Pgs: 31-35

HW: Pgs: #36-37

DAY 8: (Overall Review)

Pgs: 38-43

1

Day 1 – Bisectors and Medians 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.

Given:

then _____ _____ and _____ _____

The converse is also true:

Example 1:

Find AB.

Example 2:

Find WZ.

3

You Try It!

4

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

5

Using the CENTROID THEOREM

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

Ex 5: You Try It!

6

Ex 6: ALGEBRA

Ex 7: You Try It!

7

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.

Challenge

8

SUMMARY

9

Exit Ticket

Day 1 – HW

10

11

Equation of the Perpendicular Bisector

12

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)

13

Regents Practice

Algebra Related Question

14

Regents Practice

Algebra Related Question

15

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.

Algebra Related Question

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?

____________ _____ ___ ________

Regents Related Question

16

Challenge

SUMMARY

17

Day 2 – HW

Special Segments in Triangles

____________ __________________________________________ ____________

7)

8)

18

Points of Concurrency

19

20

Day 3 – Midsegments of Triangles

Warm - Up

21

22

9.

10.

11.

12

23

Practice

4. Find the value of n.

Find the mAMN.

24

SUMMARY

Challenge:

Exit Ticket

25

Day 3 - Homework

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

26

Day 4 – 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 ________________.

27

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.

28

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.

29

14. Use the diagram below to find FG.

15. Write an equation of the perpendicular bisector of the segment with endpoints P(3, 1) and Q(5, 5).

16.

17.

30

31

Day 5 – 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.

32

You Try It!

Example 3:

Example 4:

Example 5: Find the value of x and list the sides of ABC in order from shortest to longest if the

angles have the indicated measures.

33

Objective 2: Triangle Inequality Theorem

Example 6:

You Try It!

Example 7:

Example 8:

34

Example 9:

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

35

SUMMARY

Exit Ticket

36

Day 5 – HW

37

38

Day 6 – Overall Review

39

40

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.

41

18.

19.

20.

42

REVIEW OF POINTS OF CONCURRENCY

43