Download Unit 5 Packet

Name _________________________________________
Period ____
10/22 – 11/1
GEOMETRY UNIT 5 – TRIANGLE PROPERTIES
Vocabulary Terms:
Acute Triangle
Right Triangle
Obtuse Triangle
Scalene
Isosceles
Equilateral
Equiangular
Interior Angle
Exterior Angle
10/22
Classify and Triangle
Angle Theorems
10/29
Triangle Inequalities
Auxiliary Line
Vertex
Side
Remote Interior
Angle
Leg
Base
Base Angle
Opposite
10/23
Isosceles and Equilateral
Vertex Angle
Height
Altitude
Midsegment
Perpendicular
Bisector
Angle Bisector
Median
Centroid
10/24 – 25
Special Segments
10/30
10/31 – 11/1
Review
Incenter
Orthocenter
Circumcenter
Inequalities
Range of numbers
Inscribed
Circumscribed
Point of Concurrency
10/26
Special Segment Proofs
Test
Monday, 10/22
Chapter 4 Section 1 and 2: Classifying Triangles and Interior and Exterior Angle Theorem
I can classify a triangle by its sides or angles.
I can solve problems involving the interior triangle sum theorem.
I can solve problems involving the exterior triangle theorem
ASSIGNMENT: Pg. 219 #1-2, 12-17, 23-28, 34-37 & pg. 227 #2, 4-11, 23-24, 29-35
Completed:
Tuesday, 10/23
Chapter 4 Section 8: Isosceles and Equilateral Triangle Properties
I can solve problems using the isosceles triangle properties
I can solve problems using the equilateral triangle properties.
ASSIGNMENT: Pg. 276 (#1-7, 10, 12-13, 22-26, 28, 33-34, 44)
Completed:
Wednesday or Thursday, 10/24 – 25
Chapter 5 Section 1 – 4 : All Special Segments
I can solve problems using the midsegment of a triangle
I can find the point(s) of concurrency of a triangle
I can solve problems using the centroid, circumcenter, or incenter of a triangle.
ASSIGNMENT: Special Segments in Triangles Worksheet
Completed:
Friday, 10/26
Chapter 5 Section 1 – 4 : All Special Segments
I can use the coordinate plane to represent geometric figures.
I can use logical reasoning to prove statements are true or find a counter example to prove them false.
I can provide and recognize a valid deductive argument.
ASSIGNMENT: Special Segments on a Coordinate Plane
Completed:
Monday, 10/29
Chapter 5 Section 5 : Inequalities in 1 Triangle
I can determine if 3 segments will make a triangle
I can provide a range of answers given 2 sides of a triangle.
I can order the sides of a triangle given the angles and order the angles given the sides.
ASSIGNMENT: Pg. 336 (4-15, 32-33, 35-38, 42-53, 71)
Completed:
Tuesday, 10/30
Review Day
Completed:
ASSIGNMENT: Review Worksheet
Wednesday or Thursday, 10/31 – 11/1
Test Day
Unit 5Test: Triangle Properties
Grade:
If you miss the review day, you are still expected to take the test on the test day.
For more help BEFORE the test:
1. Use the indicated chapters in your book
2. Use the book online (it has videos and a homework help section)
3. Use Google to find more resources
4. Come to tutoring (with assignment)
Day 1
Classifying Triangles
1. Classify the triangles below based on their angle measures.
2. Classify the triangles below based on their side lengths. Diagram the triangles.
Important Note: In an __________________ triangle, all 3 angles are _________________.
In an__________________ triangle, the _____________ __________________ are congruent.
Triangle Sum Theorem and Exterior Angle Theorem
The sum of all _______________ angles in a triangle is ______________.
Ex: One acute angle of a right triangle measures 22.9⁰. Find the measure of the other acute angle.
You Try: Find the measure of the missing angle.
You Try: Find the measure of the missing angles.
50⁰
37⁰
47⁰
The measure of an __________________ angle of a triangle is equal to the sum of its ______________________
__________________ angles.
Ex: Find the measure of
Ex: Find the measure of
You Try: Solve for x.
Day 2
Isosceles and Equilateral Triangles
Objectives:
Prove theorems about isosceles and equilateral triangles.
Apply properties of isosceles and equilateral triangles.
Vocabulary:
legs of an isosceles triangle
vertex angle
base
base angles
ISOSCELES TRIANGLES
Example 1: Astronomy Application
The length of YX is 20 feet.
Explain why the length of YZ is the same.
Example 2A: Finding the Measure of an Angle
Find m∠
∠F.
Example 2B: Finding the Measure of an Angle
Find m∠
∠G.
EQUILATERAL TRIANLGES
Example 3A: Using Properties of Equilateral Triangles
Find the value of x.
Example 3B: Using Properties of Equilateral Triangles
Find the value of y.
Day 3
Special Segments Practice
I. Matching: Match the picture to the special segment. You will use the special segment more than once.
1) Midsegment
A
C
B
D
E
2) Altitude
3) Angle Bisector
F
G
4) Perpendicular Bisector
H
I
J
5) Median
II. Matching: Match the point of concurrency to the special segment and to the correct fact about location.
6) Orthocenter
A) Medians
i) Equidistant from verticies
7) Incenter
B) Altitudes
ii) Equidistant from sides
8) Circumcenter
C) Angle Bisectors
iii) 2(small section) = (larger section)
9) Centroid
D) Perpendicular Bisectors
iv) No location fact
III. Solve: Use the properties of special segments to solve the following problems.
10) Find WY, ZY, and XY
11) N is the circumcenter.
Find QN, RN, QR
2.5
12) Use the picture at the right to answer the following questions.
a) A segment parallel to AC
b) A segment that has half the length of AC
c) A segment that has twice the length of EC
13) In the diagram of ΔABC shown below, D is the midpoint of AB , E is the midpoint of BC, and F is the
midpoint of AC .
If AB = 20, BC = 12, and AC = 16, what is the perimeter of trapezoid ABEF?
A 24
B 36
C 40
D 44
14) G is the centroid. If CG = 20, find GE and CE?
15) In ΔABC shown below, P is the centroid and BF = 18. What is the length of BP?
A6
B9
C3
D 12
Use the picture to the right for 16 and 17.
16) If DF = 13, what is DE?
17) mEAD = 15° Find m<DAG and m<GAE
18) Find m<XRQ, m<PRQ, and m<PQR.
19) Find n
20) Y is the circumcenter.
Find YC and AB.
21)
22) The circumcenter of the triangle is equidistant from the ________________ of the triangle.
23) The incenter is important because it is _______________________ from the sides of the triangle.
24) Use the picture at the right to answer the following questions.
a) ST ______
d) QR ______
b) PU ______
e) m<SUP ______
c) M<SUR _______
f) m<PRQ
25.
26.
27.
Day 4
Triangles on the Coordinate Plane Examples
Ex. 1 – Classify by angles and sides.
Together: D(1, 0) E(-3, -2) W(-1, 4)
You try : F(-2, 1) O(-1, 5) G(2, 5)
Ex 2 – Midsegment –
Together: A(-3, 2) B(3, 2) C(5, -2)
You try: Find the other 2 midsegments.
Ex. 3 – Medians
Together: (-3, 2) (1, -6) (5, -2)
You try: Find the other 2 medians.
Where is the centroid?
Ex 4 – Altitude
Together:
(-2, 5) (6, 5) (4, -1)
You try: Find the other 2 altitudes.
Where is the orthocenter?
Ex. 5 – Perpendicular Bisectors
Together: (3, 3) (3, -1) (-3, -3)
Where is the circumcenter?
You try : Find the other 2 perpendicular bisectors.
Name ______________________________________ Period _______________
Special Segments on a Coordinate Plane
Classify the following triangles. Be sure to justify each classification.
1. A(1, 3) B(3, -1) C(5, 3)
2. D(-2, 3) E(4, 5) F(0, -3)
Using the points given, draw in each median. State the location of the centroid of each triangle.
3. G(-1, -3) H(7, 1) J(3, 5)
4. K(-3, 5) L(3, 1) M(-5, -3)
Using the points given, draw in each altitude. State the location of the orthocenter of each triangle.
5. (-2, 0) (4, 0) (2, 4)
6. (-3, 1) (3, 1) (1, 5)
Using the points given, draw in each perpendicular bisector. State the location of the circumcenter for
each triangle.
7. (-2, -1) (2, -3) (0, 3)
8. (-3, -2) (1, 6) (5, -2)
Using the points given, draw each midsegment. Then show that the midsegments are parallel and ½ the
length of the sides.
9. A(1, 3) B(3, -1) C(5, 3)
10. D(-2, 3) E(4, 5) F(0, -3)
NAME____________________________________DATE_________________PER.________
TRIANGLE INEQUALITY PROPERTIES NOTES
Is it possible for a triangle to have sides with the following lengths? If YES, classify the triangle by
its sides.
1. YES
or
Side lengths: 20, 9, 8
NO
Classification:____________________
2. YES
or
NO
Side lengths: 3, 4, 5
Classification:____________________
3. YES
or
NO
Side lengths: 9, 12, 15
Classification:____________________
4. YES
or
NO
Side lengths: 6, 6, 20
Classification:____________________
Given two sides of a triangle, state the range of possible values for the third side of the triangle.
6. __________________
Side lengths: 13 and 24
7. __________________
Side lengths: 6 and 21
List the segments in the following triangles shortest to longest.
8. __________
A 70°
C
65°
B
A
10. __________
40°
B
40°
C
A
11. __________
10°
150°
B
C
List the angles in the following triangles from largest to smallest.
A
12. __________
13
11
C
12
B
Y
13. __________
2
1
Z
4
X