Download Unit 3: Theorems about Triangles and Parallelograms

Unit 3: Theorems about
Triangles and Parallelograms
Geometric Concepts
Name:
Unit 3 – Theorems about Triangles and Parallelograms
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4.1/4.2
Pg 176 12-28 evens, 42-44, 54, 55
Pg 182 #2-14 evens, 18-21, 25, 26
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4.3
Pg 188 #1, 7-15, 17-25, 33, 34, 36, 40
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Review 4.1-4.3
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Quiz 4.1-4.3
4.6
Pg 209 #1, 2, 4-9, 11-16, 22-29
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7.5
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Review 4.6/7.5
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Quiz 4.6 & 7.5
6.1
Pg 306 #1-20, 24-27, 30-36
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6.2
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Quiz 6.1-6.2
6.3
Pg 320 #5-19, 28-44 evens
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6.4
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Review
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Unit 3 Test
Worksheet 4.1B, 4.2B, 4.3B
Pg 390 #2, 24-29, 33-37, 44-52 evens
Worksheet 4.6B & 5.4A (7.5)
Pg 313 #1, 10-33, 42, 43, 48, 50, 52
Pg 328 #1-12, 14-20, 27-31
TBA
Lesson 4.1 – Classifying Triangles and Lesson 4.2 – Angle Measures of Triangles
Objectives: Classify triangles by their sides and angles. Find angle measures in triangles.
DEF: Interior Angles -
DEF: Exterior Angles -
Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle is 180°
A + B + C = 180°
Exterior Angle Theorem
The exterior angle is equal to the sum of the two non-adjacent
interior angles
A + B = 1
HW: Pg 176 #12-28 evens, 42-44, 54, 55 and Pg 182 #2-14 evens, 18-21, 25, 26
Lesson 4.3 – Isosceles and Equilateral Triangles
Objectives: Use properties of isosceles and equilateral triangles.
Parts of an Isosceles Triangle
Base Angles Theorem (and its Converse)
Equilateral-Equiangular Theorems
HW: Pg 188 #1, 7-15, 17-25, 33, 34, 36, 40
Lesson 4.6 – Medians of a Triangle
Objectives: Identify medians in triangles.
DEF: Median of a triangle -
DEF: Centroid -
Examples!
BD is a median of ∆ABC.
Find DC & AC.
Q is the centroid of ∆ABC.
Find CQ and QD.
HW: Pg 209 #1, 2, 4-9, 11-16, 22-29
F is the centroid of ∆RST. Find TF and TQ.
Find BD and ED if BD = 15
and E is the centroid.
Lesson 7.5 – Midsegments of a Triangle
Objectives: Use the Triangle Proportionality Theorem and its converse.
DEF: Midsegment of a triangle -
HW: Pg 390 #2, 24-29, 33-37, 44-52 evens
Lesson 6.1 – Polygons
Objectives: Identify and classify polygons. Find angle measures of quadrilaterals.
DEF: Polygon - _________________________________________________________________________
Example!
Which figures below are polygons? Explain!
Number of
Sides
Type of Polygon
Number of
Sides
3
8
4
N
5
9
6
10
7
12
Type of Polygon
More Examples!!
Decide whether the figure is a polygon. If so, tell what type. If not, explain why.
Interior Angles of a Quadrilateral Theorem
The sum of the interior angles of a quadrilateral is __________.
Last two examples!!! 
Find mA. ________
Find the value of x. ________
HW: Pg 306 #1-20, 24-27, 30-36
Lesson 6.2 – Properties of Parallelograms (
Objectives: Use properties of parallelograms.
DEF: Parallelogram - ___________________________________
____________________________________________________
**If a Quad is a parallelogram, then…

_____________________________________________

_____________________________________________

_____________________________________________

_____________________________________________

_____________________________________________
)
Examples!
Find the value of x and y in each parallelogram.
x = _______ y = _______
x = _______ y = _______
x = _______ y = _______
x = _______ y = _______
HW: Pg 313 #1, 10-33, 42, 43, 48, 50, 52
Lessons 6.3 – Showing Quadrilaterals are Parallelograms
Objectives: Show that a quadrilateral is a parallelogram
**There are _____ ways to show that a quad is a parallelogram:
1. If opposite sides are ___________________ then the quad is a
.
2. If opposite sides are ___________________ then the quad is a
.
3. If both opposite angle pairs are ____________________ then the quad is a
4. If consecutive angles are ____________________ then the quad is a
.
5. If diagonals ___________________________________ then the quad is a
Examples!
Are these quads parallelograms? Explain.
HW: Pg 320 #5-19, 28-44 evens
.
.
Lesson 6.4 – Rhombuses, Rectangles, and Squares
Objectives: Use properties of special types of parallelograms
Rhombus: _______________________________
________________________________________
Properties:


Diagonals are _______________
Same as a parallelogram
Rectangles: ______________________________
________________________________________
Properties:


Diagonals are _______________
Same as a parallelogram
Square: ________________________________
_______________________________________
Properties:



Same as a rhombus
Same as a rectangle
Same as a parallelogram
Examples!!
Find the values of the variables.
HW: Pg 328 #1-12, 14-20, 27-31