Geometry 4-2 Complete Lesson: Triangle Congruence by SSS and SAS

By Matt Richardson

Last updated about 3 years ago

Note from the author:

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

Solve It! Are the triangles shown congruent?

How do you know?

Take Note: Summarize The Side-Side-Side (SSS) Postulate.

Take Note: Triangles are rigid figures. What does that mean?

Problem 1 Got It? Complete the proof on the canvas.

You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Take Note: In a triangle, what is an included side? What is an included angle? You may use the canvas to illustrate your responses.

Take Note: Summarize The Side-Angle-Side (SAS) Postulate.

Problem 2 Got It?

Problem 3 Got It?

Compare and Contrast: How are the SSS Postulate and the SAS Postulate alike? How are they different?

Reasoning: A carpenter trims a triangular peak of a house with three 7-ft pieces of molding. The carpenter uses 21 ft of molding to trim a second triangular peak. Are the two triangles formed congruent? Explain. You may use the canvas to help illustrate your thinking.

Review Lesson 4-1: Two quadrilaterals are congruent as described in the congruence statement below.
Match corresponding parts from the quadrilaterals.

\overline{HE}		\angle{E}
\angle{A}		\overline{AB}
\angle{GFE}		\angle{C}
\angle{G}		\overline{DA}
\overline{EF}		\angle{CBA}

Review Lesson 2-2: Write the converse of the statement. Determine whether the statement and its converse are true or false.

If x = 3, then 2x = 6.

Review Lesson 2-2: Is the converse of the statement true or false?

If x = 3, then x² = 9.

Review Lesson 4-2: In △JHK, name the side that is included between ∠J and ∠H.

Review Lesson 4-2: In △NLM, name the angle that is included between side NM and side LN.

Vocabulary Review: Use the diagram below to match corresponding items.
You may need to zoom out to see all of the items. You can also match each item from the left column by selecting it (click it) then selecting (clicking on) the mate for it.

included side between \angle{B} and \angle{A}		\angle{A}
included side between \angle{B} and \angle{C}		\overline{CA}
included side between \angle{A} and \angle{C}		\angle{C}
included angle between \overline{AB} and \overline{CA}		\overline{BC}
included angle between \overline{BC} and \overline{CA}		\angle{B}
included angle between \overline{BC} and \overline{AB}		\overline{}

Geometry 4-2 Complete Lesson: Triangle Congruence by SSS and SAS

Solve It! Are the triangles shown congruent?

How do you know?

Take Note: Summarize The Side-Side-Side (SSS) Postulate.

Take Note: Triangles are rigid figures. What does that mean?

Problem 1 Got It? Complete the proof on the canvas.

You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Take Note: In a triangle, what is an included side? What is an included angle? You may use the canvas to illustrate your responses.

Take Note: Summarize The Side-Angle-Side (SAS) Postulate.

Problem 2 Got It?

Problem 3 Got It?

Compare and Contrast: How are the SSS Postulate and the SAS Postulate alike? How are they different?

Reasoning: A carpenter trims a triangular peak of a house with three 7-ft pieces of molding. The carpenter uses 21 ft of molding to trim a second triangular peak. Are the two triangles formed congruent? Explain. You may use the canvas to help illustrate your thinking.

Review Lesson 4-1: Two quadrilaterals are congruent as described in the congruence statement below.
Match corresponding parts from the quadrilaterals.

Review Lesson 2-2: Write the converse of the statement. Determine whether the statement and its converse are true or false.

If x = 3, then 2x = 6.

Review Lesson 2-2: Is the converse of the statement true or false?

If x = 3, then x² = 9.

Review Lesson 4-2: In △JHK, name the side that is included between ∠J and ∠H.

Review Lesson 4-2: In △NLM, name the angle that is included between side NM and side LN.

Vocabulary Review: Use the diagram below to match corresponding items.
You may need to zoom out to see all of the items. You can also match each item from the left column by selecting it (click it) then selecting (clicking on) the mate for it.

Use Your Vocabulary: What is a postulate?

Reflection: Math Success

Geometry 4-2 Complete Lesson: Triangle Congruence by SSS and SAS

Solve It! Are the triangles shown congruent?

How do you know?

Take Note: Summarize The Side-Side-Side (SSS) Postulate.

Take Note: Triangles are rigid figures. What does that mean?

Problem 1 Got It? Complete the proof on the canvas.You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Take Note: In a triangle, what is an included side? What is an included angle? You may use the canvas to illustrate your responses.

Take Note: Summarize The Side-Angle-Side (SAS) Postulate.

Problem 2 Got It?

Problem 3 Got It?

Compare and Contrast: How are the SSS Postulate and the SAS Postulate alike? How are they different?

Reasoning: A carpenter trims a triangular peak of a house with three 7-ft pieces of molding. The carpenter uses 21 ft of molding to trim a second triangular peak. Are the two triangles formed congruent? Explain. You may use the canvas to help illustrate your thinking.

Review Lesson 4-1: Two quadrilaterals are congruent as described in the congruence statement below. Match corresponding parts from the quadrilaterals.

Review Lesson 2-2: Write the converse of the statement. Determine whether the statement and its converse are true or false. If x = 3, then 2x = 6.

Review Lesson 2-2: Is the converse of the statement true or false? If x = 3, then x² = 9.

Review Lesson 4-2: In △JHK, name the side that is included between ∠J and ∠H.

Review Lesson 4-2: In △NLM, name the angle that is included between side NM and side LN.

Vocabulary Review: Use the diagram below to match corresponding items. You may need to zoom out to see all of the items. You can also match each item from the left column by selecting it (click it) then selecting (clicking on) the mate for it.

Use Your Vocabulary: What is a postulate?

Reflection: Math Success

Problem 1 Got It? Complete the proof on the canvas.

You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Review Lesson 4-1: Two quadrilaterals are congruent as described in the congruence statement below.
Match corresponding parts from the quadrilaterals.

Review Lesson 2-2: Write the converse of the statement. Determine whether the statement and its converse are true or false.

If x = 3, then 2x = 6.

Review Lesson 2-2: Is the converse of the statement true or false?

If x = 3, then x² = 9.

Vocabulary Review: Use the diagram below to match corresponding items.
You may need to zoom out to see all of the items. You can also match each item from the left column by selecting it (click it) then selecting (clicking on) the mate for it.