triangle properties part a - white plains middle · pdf fileopposite side. every triangle has...
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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
1
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 = ______________
11
9.
12
10.
Vocabulary Recap
13
SUMMARY
14
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
19
Ex 5: You Try It!
Ex 6: ALGEBRA
Ex 7: You Try It!
20
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
22
Challenge
Exit Ticket
23
Day 3 – HW
24
25
Day 4 – Midsegments of Triangles
Warm - Up
26
27
9.
10.
11.
12
28
Practice
4. Find the value of n.
Find the mAMN.
29
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.
34
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.
35
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!
38
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
39
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.
44
12.
13.
14.
15.
16.
17.
45
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
47
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.
48
26
27
28
49
Day 8 – Overall Review
50
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.
53
21. Review Ch art and answer questions below.
54