Geometry 7-3 Complete Lesson: Proving Similar Triangles

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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.

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Geometry 7-3 Complete Lesson: Proving Similar Triangles

Geometry 7-3 Complete Lesson: Proving Similar Triangles

Solve It! Are the triangles similar? (Hint: Use a centimeter ruler to measure the sides of each triangle.)

Problem 1 Got It? Are the two triangles similar?

Problem 2 Got It? Are the two triangles similar?

Problem 2 Got It? Are the two triangles similar?

Problem 3 Got It? Complete the proof on the canvas.

Problem 3 Got It? Reasoning: For the figure in the previous item, suppose that your are given only that the following proportion is true. Could you prove that the triangles are similar?

Problem 3 Got It? Reasoning: Explain your response to the previous item.

Problem 4 Got It? Reasoning: Why is it important that the ground be flat to use the method of indirect measurement illustrated in Problem 4? Explain.

Vocabulary: How could you use indirect measurement to find the height of the flagpole at your school?

Error Analysis: Which solution for the value of x in the figure is not correct?

Error Analysis: Explain your response to the previous item.

Compare and Contrast: How are the SAS Similarity Theorem and the SAS Congruence Postulate alike? How are they different?

Compare and Contrast: How are the SSS Similarity Theorem and the SSS Congruence Postulate alike? How are they different?

Review Lesson 7-2: TRAP ~ EZYD. Find the scale factor of TRAP to EZYD.

Review Lesson 1-4: Classify each angle as acute, right, obtuse, or straight. You may use a protractor if necessary.

Review Lesson 7-1: Identify the means of the proportion. Select all that apply.

Review Lesson 7-1: Identify the extremes of the proportion. Select all that apply.

Review Lesson 7-1: Solve the proportion for x. Round to the nearest hundredth if necessary.

Vocabulary Review: Write the converse of the theorem. If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

Use Your Vocabulary: True or False: You can verify that two triangles are similar by showing that corresponding angles are proportional.

Use Your Vocabulary: True or False: You can use properties, postulates, and previously proven theorems to verify steps in a proof.

Reflection: Math Success

Solve It! Are the triangles similar? (Hint: Use a centimeter ruler to measure the sides of each triangle.)

Problem 1 Got It? Are the two triangles similar?

How do you know?

Problem 1 Got It? Are the two triangles similar?

Problem 2 Got It? Are the two triangles similar?

Problem 2 Got It? If they are similar, which similarity statement describes the relationship?

Problem 2 Got It? Are the two triangles similar?

Problem 2 Got It? If they are similar, which similarity statement describes the relationship?

Problem 3 Got It? Complete the proof on the canvas.

Problem 3 Got It? Reasoning: For the figure in the previous item, suppose that your are given only that the following proportion is true. Could you prove that the triangles are similar?

Problem 3 Got It? Reasoning: Explain your response to the previous item.

Problem 4 Got It? Reasoning: Why is it important that the ground be flat to use the method of indirect measurement illustrated in Problem 4? Explain.

Vocabulary: How could you use indirect measurement to find the height of the flagpole at your school?

Error Analysis: Which solution for the value of x in the figure is not correct?

Error Analysis: Explain your response to the previous item.

Compare and Contrast: How are the SAS Similarity Theorem and the SAS Congruence Postulate alike? How are they different?

Compare and Contrast: How are the SSS Similarity Theorem and the SSS Congruence Postulate alike? How are they different?

Review Lesson 7-2: TRAP ~ EZYD. Find the scale factor of TRAP to EZYD.

Review Lesson 7-2: TRAP ~ EZYD. Find m∠R. Enter only a number.

Review Lesson 7-2: TRAP ~ EZYD. Find DY. Enter only a number.

Review Lesson 7-2: TRAP ~ EZYD. Find the ratio. Enter only a number. Use decimal form.

Review Lesson 1-4: Classify each angle as acute, right, obtuse, or straight. You may use a protractor if necessary.

Review Lesson 7-1: Identify the means of the proportion. Select all that apply.

Review Lesson 7-1: Identify the extremes of the proportion. Select all that apply.

Review Lesson 7-1: Solve the proportion for x. Round to the nearest hundredth if necessary.

Vocabulary Review: Write the converse of the theorem. If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

Use Your Vocabulary: True or False: You can verify that two triangles are similar by showing that corresponding angles are proportional.

Use Your Vocabulary: True or False: You can use properties, postulates, and previously proven theorems to verify steps in a proof.

Reflection: Math Success

How do you know?

Problem 1 Got It? Are the two triangles similar?

Problem 2 Got It? If they are similar, which similarity statement describes the relationship?

Problem 2 Got It? If they are similar, which similarity statement describes the relationship?

Review Lesson 7-2: TRAP ~ EZYD. Find m∠R. Enter only a number.

Review Lesson 7-2: TRAP ~ EZYD. Find DY. Enter only a number.

Review Lesson 7-2: TRAP ~ EZYD. Find the ratio. Enter only a number. Use decimal form.

Problem 3 Got It? Reasoning: For the figure in the previous item, suppose that your are given only that the following proportion is true.
Could you prove that the triangles are similar?

Review Lesson 7-1: Identify the means of the proportion.
Select all that apply.

Review Lesson 7-1: Identify the extremes of the proportion.
Select all that apply.

Review Lesson 7-1: Solve the proportion for x.
Round to the nearest hundredth if necessary.

Vocabulary Review: Write the converse of the theorem.
If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

Problem 3 Got It? Reasoning: For the figure in the previous item, suppose that your are given only that the following proportion is true.
Could you prove that the triangles are similar?

Review Lesson 7-2: TRAP ~ EZYD. Find the ratio.
Enter only a number. Use decimal form.

Review Lesson 7-1: Identify the means of the proportion.
Select all that apply.

Review Lesson 7-1: Identify the extremes of the proportion.
Select all that apply.

Review Lesson 7-1: Solve the proportion for x.
Round to the nearest hundredth if necessary.

Vocabulary Review: Write the converse of the theorem.
If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

Review Lesson 7-2: TRAP ~ EZYD. Find the ratio.
Enter only a number. Use decimal form.