Geometry 2-6 Complete Lesson: Proving Angles Congruent

Solve It! A quilter wants to duplicate this quilt, but knows the measure of only two angles.
What are the measures of angles 1, 2, 3, and 4? How do you know?

Take Note: Define theorem.

Take Note: Summarize the Vertical Angles Theorem. You may use the canvas to help illustrate your explanation.

Problem 1 Got It?
What is the value of x?

Problem 2 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.

Problem 2 Got It? Reasoning: How can you prove ∠1 ≅ ∠2 ≅ ∠3 ≅ ∠4 without using the Vertical Angles Theorem? Explain in the response field.

You may use the canvas to help illustrate your explanation.

Take Note: Describe paragraph proofs. How are they similar to two-column proofs? How are they different?

Take Note: Summarize the Congruent Supplements Theorem. You may use the canvas to help illustrate your explanation.

Problem 3 Got It? Write a paragraph proof for the Vertical Angles Theorem in the response field.

You may use the canvas to construct the related two-column proof.

Take Note: Summarize the Congruent Complements Theorem. You may use the canvas to help illustrate your explanation.

Take Note: SummarizeTheorem 2-4, which states: All right angles are congruent. You may use the canvas to help illustrate your explanation.

Take Note: SummarizeTheorem 2-5, which states: If two angles are congruent and supplementary, then each is a right angle. You may use the canvas to help illustrate your explanation.

Reasoning: If ∠A and ∠B are supplements, and ∠A and ∠C are supplements, what can you conclude about ∠B and ∠C? Explain.

Error Analysis: Your friend knows that ∠1 and ∠2 are complementary and that ∠1 and ∠3 are complementary. He concludes that ∠2 and ∠3 must be complementary. What is his error in reasoning?

Compare and Contrast: How is a theorem different from a postulate?

Review Lesson 2-5: Match each pair of statements on the left with the property of equality or congruence that justifies going from the first statement to the second.

Review Lesson 1-2: Refer to the figure below. Respond to each item on the right using the correct item from the left.

SAT/ACT: ∠1 and ∠2 are vertical angles. if m∠1 = 63 and m∠2 = 4x - 9, what is the value of x?
Enter only a number.

SAT/ACT: What is the area in square centimeters of a triangle with a base of 5 cm and a height of 8 cm?

Vocabulary Review: Complete each sentence on the right with the word proof or prove from the left.

Use Your Vocabulary: Tag each statement on the right as true or false.

Use Your Vocabulary: Complete each sentence on the right with the word lines, planes, or points from the left.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

Solve It! A quilter wants to duplicate this quilt, but knows the measure of only two angles. What are the measures of angles 1, 2, 3, and 4? How do you know?

Take Note: Define theorem.

Take Note: Summarize the Vertical Angles Theorem. You may use the canvas to help illustrate your explanation.

Problem 1 Got It?What is the value of x?

Problem 2 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.

Problem 2 Got It? Reasoning: How can you prove ∠1 ≅ ∠2 ≅ ∠3 ≅ ∠4 without using the Vertical Angles Theorem? Explain in the response field. You may use the canvas to help illustrate your explanation.

Take Note: Describe paragraph proofs. How are they similar to two-column proofs? How are they different?

Take Note: Summarize the Congruent Supplements Theorem. You may use the canvas to help illustrate your explanation.

Problem 3 Got It? Write a paragraph proof for the Vertical Angles Theorem in the response field. You may use the canvas to construct the related two-column proof.

Take Note: Summarize the Congruent Complements Theorem. You may use the canvas to help illustrate your explanation.

Take Note: SummarizeTheorem 2-4, which states: All right angles are congruent. You may use the canvas to help illustrate your explanation.

Take Note: SummarizeTheorem 2-5, which states: If two angles are congruent and supplementary, then each is a right angle. You may use the canvas to help illustrate your explanation.

Reasoning: If ∠A and ∠B are supplements, and ∠A and ∠C are supplements, what can you conclude about ∠B and ∠C? Explain.

Error Analysis: Your friend knows that ∠1 and ∠2 are complementary and that ∠1 and ∠3 are complementary. He concludes that ∠2 and ∠3 must be complementary. What is his error in reasoning?

Compare and Contrast: How is a theorem different from a postulate?

Review Lesson 2-5: Match each pair of statements on the left with the property of equality or congruence that justifies going from the first statement to the second.

Review Lesson 1-2: Refer to the figure below. Respond to each item on the right using the correct item from the left.

SAT/ACT: ∠1 and ∠2 are vertical angles. if m∠1 = 63 and m∠2 = 4x - 9, what is the value of x?Enter only a number.

SAT/ACT: What is the area in square centimeters of a triangle with a base of 5 cm and a height of 8 cm?

Vocabulary Review: Complete each sentence on the right with the word proof or prove from the left.

Use Your Vocabulary: Tag each statement on the right as true or false.

Use Your Vocabulary: Complete each sentence on the right with the word lines, planes, or points from the left.You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

Reflection: Math Success

Solve It! A quilter wants to duplicate this quilt, but knows the measure of only two angles.
What are the measures of angles 1, 2, 3, and 4? How do you know?

Problem 1 Got It?
What is the value of x?

Problem 2 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.

Problem 2 Got It? Reasoning: How can you prove ∠1 ≅ ∠2 ≅ ∠3 ≅ ∠4 without using the Vertical Angles Theorem? Explain in the response field.

You may use the canvas to help illustrate your explanation.

Problem 3 Got It? Write a paragraph proof for the Vertical Angles Theorem in the response field.

You may use the canvas to construct the related two-column proof.

SAT/ACT: ∠1 and ∠2 are vertical angles. if m∠1 = 63 and m∠2 = 4x - 9, what is the value of x?
Enter only a number.

Use Your Vocabulary: Complete each sentence on the right with the word lines, planes, or points from the left.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.