1Congruent and Similar Triangles
On the GED^{®} Mathematics Test, students may need to solve problems related to congruent triangles or similar triangles.
 Students will need to recognize that triangles are congruent, even if they are rotated differently.
 They will also need to recognize similar triangles and utilize proportions to find unknown sides.
This lesson covers the principles of congruence and similarity in triangles. Students often have difficulty applying these skills in complex drawings and realistic contexts.
Note: On the GED Mathematics Test, students will not be asked to produce answers that require recall of terminology.
2Congruent Triangles
Angles or side lengths are congruent when they have the same measures.
 Congruent triangles have the same shape and size. Their corresponding sides and angles are equal. In diagrams, congruent parts are marked with the same symbols (I II III).
 There are six corresponding parts in two congruent triangles. If you know that three of these parts are congruent, you can prove the triangles are congruent.
SideSideSide (SSS) Three corresponding sides are congruent.
SideAngleSide (SAS) Two sides and the angle between them are congruent.
AngleSideAngle (ASA) Two angles and the side between them are congruent.
Question Are these triangles congruent or not? Explain how you know.
Step 1 Look for pairs of congruent parts.
∠M = ∠R; side MO = side RO; ∠NOM = ∠POR
Step 2 Choose SSS, SAS, or ASA to prove the triangles are congruent.
The congruent sides are between the two pairs of congruent angles. This is anglesideangle, or ASA, property.
Answer The triangles are congruent because of ASA.
3Similar Triangles
Triangles: Similar
Video: 0m 54s
 Similar triangles have the same shape, but they are not necessarily the same size. Their corresponding angles are equal, and their corresponding sides are in proportion to each other—they have the same ratio.
 A proportion is an equation with two equal ratios. A proportion can be used to find a missing side length in a pair of similar triangles. Use the three given sides, and solve for the missing side length.
Question Henry wants to find the height of the tree in his front yard. With his son’s help, he measures his own shadow and the shadow of the tree. Henry is 6 feet tall.
What is the height of the tree?
Step 1 Organize the given facts in a table. Use h for the height of the tree. That is the number you need to find.
Step 2 Write a proportion based on the table.
Step 3 Find the cross products. Then divide by the remaining term to isolate h.
h× 10 = 6 × 60
h× 10 ÷ 10 = 360 ÷ 10
h = 36
Answer 36 feet
4Sample GED Questions
Directions: There are two questions on this page. Each will appear in the blue rectangle below. Click on Question 1 to see the first question, and then select your answer. Click on Question 2 to see the second question, and select your answer. As you solve these problems, also respond to the question below, which is related to building students’ skills.
How could you help students see that there are two similar triangles combined in the figure in Question 2?
Click for more teaching ideas.
5Skill Review
Lines, Angles, and Triangles: Congruent and Similar Triangles Skill Review
Document
Printable Resource
In this lesson you have learned about congruent and similar triangles. This review consists of key terms and concepts with which you will need to be familiar. Click the view button on the left to access a review sheet.
Below you will also see a Classroom Connection with suggestions for linking this geometry content with your instruction.
Return to the GED Online Professional Development Course.
Credits
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Flash programming: E. Tattershall
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Producer/Director: Vince Spoelker
Editor: Jim Piston
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Flash Programming: Dave Hamon
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PDF Layout Design: Amanda Dawahare
Congruent and Similar Triangles is the sixth of eight selfpaced lessons in the “Lines, Angles, and Triangles” section of KET’s GED^{®} Geometry Professional ...
Congruent and Similar Triangles is the sixth of eight selfpaced lessons in the “Lines, Angles, and Triangles” section of KET’s GED^{®} Geometry Professional Development Online Course. This lesson covers the principles of congruence and similarity in triangles.
Common Core State Standards

CCSS.Math.Con.HSGCO (High School  Geometry ): Congruence

CCSS.Math.Con.HSGCO.B (High School  Geometry ): Understand congruence in terms of rigid motions

CCSS.Math.Con.HSGCO.B (High School  Geometry ): Understand congruence in terms of rigid motions

CCSS.Math.Con.HSGSRT (High School  Geometry ): Similarity, Right Triangles, and Trigonometry

CCSS.Math.Con.HSGSRT.A (High School  Geometry ): Understand similarity in terms of similarity transformations

CCSS.Math.Con.HSGSRT.A (High School  Geometry ): Understand similarity in terms of similarity transformations

CCSS.Math.Con.HSGSRT (High School  Geometry ): Similarity, Right Triangles, and Trigonometry

CCSS.Math.Con.HSGSRT.A (High School  Geometry ): Understand similarity in terms of similarity transformations

CCSS.Math.Con.HSGSRT.A (High School  Geometry ): Understand similarity in terms of similarity transformations