## Proving Statements in Geometry

1. Inductive Reasoning

2. Definitions as Biconditionals

3. Deductive Reasoning

4. Direct and Indirect Proofs

5. Postulates, Theorems, and Proofs

6. The Substitution Postulate

7. The Addition and Subtraction Postulates

8. The Multiplication and Division Postulates

Standards

Prove geometric theorems

CCSS.MATH.CONTENT.HSG.CO.C.9

Prove theorems about lines and angles.

CCSS.MATH.CONTENT.HSG.CO.C.10

Prove theorems about triangles.

CCSS.MATH.CONTENT.HSG.CO.C.11

Prove theorems about parallelograms.

Prove theorems involving similarity

CCSS.MATH.CONTENT.HSG.SRT.B.4

Prove theorems about triangles.

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures

Understand and apply theorems about circles

CCSS.MATH.CONTENT.HSG.C.A.1

Prove that all circles are similar.

Use coordinates to prove simple geometric theorems algebraically

CCSS.MATH.CONTENT.HSG.GPE.B.4

Use coordinates to prove simple geometric theorems algebraically.

2. Definitions as Biconditionals

3. Deductive Reasoning

4. Direct and Indirect Proofs

5. Postulates, Theorems, and Proofs

6. The Substitution Postulate

7. The Addition and Subtraction Postulates

8. The Multiplication and Division Postulates

Standards

Prove geometric theorems

CCSS.MATH.CONTENT.HSG.CO.C.9

Prove theorems about lines and angles.

*Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints*.CCSS.MATH.CONTENT.HSG.CO.C.10

Prove theorems about triangles.

*Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point*.CCSS.MATH.CONTENT.HSG.CO.C.11

Prove theorems about parallelograms.

*Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals*.Prove theorems involving similarity

CCSS.MATH.CONTENT.HSG.SRT.B.4

Prove theorems about triangles.

*Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.**CCSS.MATH.CONTENT.HSG.SRT.B.5*Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures

Understand and apply theorems about circles

CCSS.MATH.CONTENT.HSG.C.A.1

Prove that all circles are similar.

Use coordinates to prove simple geometric theorems algebraically

CCSS.MATH.CONTENT.HSG.GPE.B.4

Use coordinates to prove simple geometric theorems algebraically.

*For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).*