Five-Minute Check (over Lesson 2–5)

CCSS

Then/Now

New Vocabulary

Key Concept: Properties of Real Numbers

Example 1: Justify Each Step When Solving an Equation

Example 2: Real-World Example: Write an Algebraic Proof

Example 3: Write a Geometric Proof

Over Lesson 2–5

A. A line contains at least two points.

B. A line contains only two points.

C. A line contains at least three points.

D. A line contains only three points.

In the figure shown, A, C, and lie in plane R, and B is on . Which option states the postulate that can be used to show that A, B, and C are collinear?

Over Lesson 2–5

A. Through two points, there is exactly one line in a plane.

B. Any plane contains an infinite number of lines.

C. Through any two points on the same line, there is exactly one plane.

D. If two points lie in a plane, then the entire line containing those points lies in that plane.

In the figure shown, A, C, and lie in plane R, and B is on . Which option states the postulate that can be used to show that lies in plane R?

Over Lesson 2–5

A. Through any two points on the same line, there is exactly one plane.

B. Through any three points not on the same line, there is exactly one plane.

C. If two points lie in a plane, then the entire line containing those points lies in that plane.

D. If two lines intersect, then their intersection lies in exactly one plane.

In the figure shown, A, C, and lie in plane R, and B is on . Which option states the postulate that can be used to show that A, H, and D are coplanar?

Over Lesson 2–5

A. Through any two points, there is exactly one line.

B. A line contains only two points.

C. If two points lie in a plane, then the entire line containing those points lies in that plane.

D. Through any two points, there are many lines.

In the figure shown, A, C, and lie in plane R, and B is on . Which option states the postulate that can be used to show that E and F are collinear?

Over Lesson 2–5

A. The intersection point of two lines lies on a third line, not in the same plane.

B. If two lines intersect, then their intersection point lies in the same plane.

C. The intersection of two lines does not lie in the same plane.

D. If two lines intersect, then their intersection is exactly one point.

In the figure shown, A, C, and lie in plane R, and B is on . Which option states the postulate that can be used to show that intersects at point B?

Over Lesson 2–5

Which of the following numbers is an example of an irrational number?

A. –7

B.

C.

D. 34

You used postulates about points, lines, and planes to write paragraph proofs.

• Use algebra to write two-column proofs.

• Use properties of equality to write geometric proofs.

• algebraic proof

• two-column proof

• formal proof

Justify Each Step When Solving an Equation

Solve 2(5 – 3a) – 4(a + 7) = 92.

A. a = 12

B. a = –37

C. a = –7

D. a = 7

Solve –3(a + 3) + 5(3 – a) = –50.

Write an Algebraic Proof

Write a Geometric Proof

If A B, mB = 2mC, and mC = 45, then mA = 90. Write a two-column proof to verify this conjecture.

• Assignment:

• 139/ 1-20,42-48,50-58