Download Triangle Congruence: SSS, SAS, and ASA, Part 1

MTH203A: Geometry | Unit 4 | Lesson 3: Triangle Congruence: SSS, SAS, and ASA, Part 1
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Student Guide
Lesson 3: Triangle Congruence: SSS, SAS, and ASA, Part 1
Bridges, ladders, containers, and other items that need to be sturdy often use triangles. A combination of triangles
is strong yet flexible. The shape of a triangle cannot change as long as the sides remain the same size. Do you
think a rectangle would provide the same stability?
Goals for This Lesson
•
Identify included angles and included sides in triangles.
•
Identify the Side-Side-Side, Side-Angle-Side, and Angle-Side-Angle Congruence Postulates.
Graded Activities in This Lesson
Lesson 3 Quiz (online, scored by computer)
Materials
“Triangle Congruence: SSS, SAS, and ASA” in Geometry: A Reference Guide
Triangle Congruence: SSS, SAS, and ASA Problem Set
Triangle Congruence: SSS, SAS, and ASA Solutions
Keywords and Pronunciations
included angle: the angle between two sides of a triangle
included side: the side between two angles of a triangle
Groundwork [online]
Make sure you understand the Polygon Congruence Postulate. In this lesson, you will focus on three-sided
polygons, more commonly called triangles.
Notes
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Page 1 of 6
MTH203A: Geometry | Unit 4 | Lesson 3: Triangle Congruence: SSS, SAS, and ASA, Part 1
Side-Side-Side Congruence Postulate [online]
Given three side lengths, any triangle that you draw will have the same size and shape.
Notes
Draw two congruent triangles. Mark three pairs of congruent sides.
Side-Angle-Side Congruence Postulate [online]
To understand the Side-Angle-Side Congruence Postulate, you need to understand the term included angle.
Notes
Draw two congruent triangles. Mark two pairs of congruent sides and one pair of included angles.
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Page 2 of 6
MTH203A: Geometry | Unit 4 | Lesson 3: Triangle Congruence: SSS, SAS, and ASA, Part 1
Angle-Side-Angle Congruence Postulate [online]
To understand the Angle-Side-Angle Congruence Postulate, you need to understand the term included side.
Notes
Draw two congruent triangles. Mark two pairs of congruent angles and one pair of included sides.
GeoGebra: Explore SSS, SAS, and ASA [offline]
Open the Explore SSS, Explore SAS, and Explore ASA worksheets in GeoGebra: Explore Triangle Congruence.
Here’s how you can explore triangle congruence with each of the constructions.
1. Each file (SSS, SAS, and ASA) corresponds to a different triangle congruence postulate. Each
construction uses circles to set lengths. Any side with a length that is not set with a slider is shown
with a ray.
2. Each construction uses circles or angles to change the triangles’ lengths.
a. Drag points on the sliders at the bottom of the Drawing Pad to increase or decrease side
lengths.
b. To change the measure of a shaded angle, drag the point at the end of the red segment on
the angle at the bottom of the screen.
3. Go through each construction and set the three measures to create different triangles. Study the way
changing a side length or angle changes the shapes of circles and the shape of the triangle.
Read the questions below and experiment with the GeoGebra constructions to determine the answers.
Questions
1. Why are set lengths created by using a circle?
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MTH203A: Geometry | Unit 4 | Lesson 3: Triangle Congruence: SSS, SAS, and ASA, Part 1
2. What tool for creating constructions can be used to create circles?
3. Study each triangle that you create. Would it be possible to create a triangle with a different size and shape
without changing one of the set measures? For example, create a triangle using the ASA construction. Can
you create a triangle with different side lengths without changing the set angles or side?
4. If any of these properties did not guarantee congruence, what do you think would happen in the construction?
Using Triangle Congruence Postulates [online]
You can use the following space to sketch the figures in this activity so you can mark additional congruent parts.
Notes
Summary [online]
In this lesson, you learned three postulates that you can use to prove congruence in triangles:
•
Side-Side-Side Postulate
•
Side-Angle-Side Postulate
•
Angle-Side-Angle Postulate
These postulates allow you to prove congruence in triangles with much less information than you needed with the
Polygon Congruence Postulate.
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MTH203A: Geometry | Unit 4 | Lesson 3: Triangle Congruence: SSS, SAS, and ASA, Part 1
Offline Learning [offline]
Read pages 105–109 in the reference guide.
Problem Sets
Complete Problems 1A, 1C, and 3–31 odd in Triangle Congruence: SSS, SAS, and ASA Problem Set.
The lesson quiz will be based on these problems.
Extra Practice (optional)
Complete Problems 1B, 1D, and 2–32 even.
Lesson Quiz [online]
Now go back online to take the lesson quiz.
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MTH203A: Geometry | Unit 4 | Lesson 3: Triangle Congruence: SSS, SAS, and ASA, Part 1
Answers to Questions
1. A set length is created by a circle because all radii of a given circle have the same length.
2. A compass is used to construct circles. In GeoGebra, you can use the Compass tool, the Circle with Center
through Point, the Circle with Center and Radius, or the Circle through Three Points tools.
3. You cannot create a triangle with a different size and shape without changing one of the set measures. Notice
that the set measures force the triangle to one size and shape. For example, if you create a triangle on the
ASA page, you can see that the set angles and sides force the other angles and sides to one measure. You
cannot create a triangle with a different shape without changing one of the set angles or the set side.
4. If a property did not guarantee congruence, then the measures you set would result in more than one possible
triangle. It would be possible to create a triangle with a different size and shape by changing one of the sides
or angles that aren't set.
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