Geometry 5-7 Complete Lesson: Inequalities in Two 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.

G.CO.10

Geometry 5-7 Complete Lesson: Inequalities in Two Triangles

Geometry 5-7 Complete Lesson: Inequalities in Two Triangles

Solve It! Think of a clock or watch that has an hour hand and a minute hand. As minutes pass, the distance between the tip of the hour hand and the tip of the minute hand changes. This distance is x in the clock shown. Sort the times below from least to greatest length of x ?

Problem 1 Got It? What inequality relates LN and OQ in the figure?

Problem 1 Got It? Reasoning: In △ABC, AB = 3, BC = 4, and CA = 6. In △PQR, PQ = 3, QR = 5, and RP = 6. How can you use indirect reasoning to explain why m∠P > m∠A ?

Problem 2 Got It? The diagram shows a pair of scissors in two different positions. In which position is the distance between the tips of the two blades greater?

Problem 2 Got It? How does the Hinge Theorem apply to this scenario?

Problem 3 Got It?

Problem 4 Got It? Complete the proof on the canvas.

Error Analysis: From the figure, your friend concludes that m∠BAD > m∠BCD. How would you correct your friend's mistake?

Compare and Contrast: How are the Hinge Theorem and the SAS Congruence Postualte similar? How are they different?

Review Lesson 5-6: Order the angles of the triangle from smallest to largest.

Review Lesson 5-6: Order the angles of the triangle from smallest to largest.

Review Lesson 5-6: Match the range of possible lengths for the third side of a triangle in the left column with the given lengths of two sides of a triangle in the right column.
Not all ranges will be used, only one per pair of side lengths.

Review Lesson 5-6: In △GHI, which side is included between ∠G and ∠H ?

Review Lesson 3-7: Match the slopes on the left with the pairs of points on the right.

Use Your Vocabulary: Identify which form of the word hinge is used in each sentence.

Reflection: Math Success

Solve It! Think of a clock or watch that has an hour hand and a minute hand. As minutes pass, the distance between the tip of the hour hand and the tip of the minute hand changes. This distance is x in the clock shown. Sort the times below from least to greatest length of x ?

Problem 1 Got It? What inequality relates LN and OQ in the figure?

Problem 1 Got It? Reasoning: In △ABC, AB = 3, BC = 4, and CA = 6. In △PQR, PQ = 3, QR = 5, and RP = 6. How can you use indirect reasoning to explain why m∠P > m∠A ?

Problem 2 Got It? The diagram shows a pair of scissors in two different positions. In which position is the distance between the tips of the two blades greater?

Problem 2 Got It? How does the Hinge Theorem apply to this scenario?

Problem 3 Got It?

Problem 4 Got It? Complete the proof on the canvas.

Error Analysis: From the figure, your friend concludes that m∠BAD > m∠BCD. How would you correct your friend's mistake?

Compare and Contrast: How are the Hinge Theorem and the SAS Congruence Postualte similar? How are they different?

Review Lesson 5-6: Order the angles of the triangle from smallest to largest.

Review Lesson 5-6: Order the angles of the triangle from smallest to largest.

Review Lesson 5-6: Match the range of possible lengths for the third side of a triangle in the left column with the given lengths of two sides of a triangle in the right column.
Not all ranges will be used, only one per pair of side lengths.

Review Lesson 5-6: In △GHI, which side is included between ∠G and ∠H ?

Review Lesson 3-7: Match the slopes on the left with the pairs of points on the right.

Use Your Vocabulary: Identify which form of the word hinge is used in each sentence.

Reflection: Math Success

Geometry 5-7 Complete Lesson: Inequalities in Two Triangles

Geometry 5-7 Complete Lesson: Inequalities in Two Triangles

Solve It! Think of a clock or watch that has an hour hand and a minute hand. As minutes pass, the distance between the tip of the hour hand and the tip of the minute hand changes. This distance is x in the clock shown. Sort the times below from least to greatest length of x ?

Problem 1 Got It? What inequality relates LN and OQ in the figure?

Problem 1 Got It? Reasoning: In △ABC, AB = 3, BC = 4, and CA = 6. In △PQR, PQ = 3, QR = 5, and RP = 6. How can you use indirect reasoning to explain why m∠P > m∠A ?

Problem 2 Got It? The diagram shows a pair of scissors in two different positions. In which position is the distance between the tips of the two blades greater?

Problem 2 Got It? How does the Hinge Theorem apply to this scenario?

Problem 3 Got It?

Problem 4 Got It? Complete the proof on the canvas.

Error Analysis: From the figure, your friend concludes that m∠BAD > m∠BCD. How would you correct your friend's mistake?

Compare and Contrast: How are the Hinge Theorem and the SAS Congruence Postualte similar? How are they different?

Review Lesson 5-6: Order the angles of the triangle from smallest to largest.

Review Lesson 5-6: Order the angles of the triangle from smallest to largest.

Review Lesson 5-6: Match the range of possible lengths for the third side of a triangle in the left column with the given lengths of two sides of a triangle in the right column. Not all ranges will be used, only one per pair of side lengths.

Review Lesson 5-6: In △GHI, which side is included between ∠G and ∠H ?

Review Lesson 3-7: Match the slopes on the left with the pairs of points on the right.

Use Your Vocabulary: Identify which form of the word hinge is used in each sentence.

Reflection: Math Success

Solve It! Think of a clock or watch that has an hour hand and a minute hand. As minutes pass, the distance between the tip of the hour hand and the tip of the minute hand changes. This distance is x in the clock shown. Sort the times below from least to greatest length of x ?

Problem 1 Got It? What inequality relates LN and OQ in the figure?

Problem 1 Got It? Reasoning: In △ABC, AB = 3, BC = 4, and CA = 6. In △PQR, PQ = 3, QR = 5, and RP = 6. How can you use indirect reasoning to explain why m∠P > m∠A ?

Problem 2 Got It? The diagram shows a pair of scissors in two different positions. In which position is the distance between the tips of the two blades greater?

Problem 2 Got It? How does the Hinge Theorem apply to this scenario?

Problem 3 Got It?

Problem 4 Got It? Complete the proof on the canvas.

Error Analysis: From the figure, your friend concludes that m∠BAD > m∠BCD. How would you correct your friend's mistake?

Compare and Contrast: How are the Hinge Theorem and the SAS Congruence Postualte similar? How are they different?

Review Lesson 5-6: Order the angles of the triangle from smallest to largest.

Review Lesson 5-6: Order the angles of the triangle from smallest to largest.

Review Lesson 5-6: Match the range of possible lengths for the third side of a triangle in the left column with the given lengths of two sides of a triangle in the right column. Not all ranges will be used, only one per pair of side lengths.

Review Lesson 5-6: In △GHI, which side is included between ∠G and ∠H ?

Review Lesson 3-7: Match the slopes on the left with the pairs of points on the right.

Use Your Vocabulary: Identify which form of the word hinge is used in each sentence.

Reflection: Math Success

Review Lesson 5-6: Match the range of possible lengths for the third side of a triangle in the left column with the given lengths of two sides of a triangle in the right column.
Not all ranges will be used, only one per pair of side lengths.

Review Lesson 5-6: Match the range of possible lengths for the third side of a triangle in the left column with the given lengths of two sides of a triangle in the right column.
Not all ranges will be used, only one per pair of side lengths.