Unit 1: Foundations of Geometry

Unit 1 Learning Targets

LT 1-1: I can determine the measure of segments and angles.

LT 1-2: I can perform basic constructions.

LT 1-3: I can find the distance between and the midpoint of 2 points.

LT 1-4: I can use inductive reasoning to make predictions.

LT 1-5: I can complete a conditional statement.

LT 1-6: I can use deductive reasoning to make an argument.

LT 1-7: I can complete a proof.

LESSON 1-1

Measuring Segments and Angles

The sum of the lengths of the smaller parts of a segment is the

length of the segment. The sum of the measures of the two smaller angles that form a larger angle is the measure of the larger angle.

Help Videos:

● What Is the Segment Addition Postulate?

● How Do You Find Angle Measures for Adjacent Angles?

Practice:

1-1 Math XL

LESSON 1-2

Basic Constructions

A construction is a geometric figure produced using only a straightedge and a compass. Constructions are useful tools for geometry.

Help Videos:

● What Does Congruent Mean?

Practice:

1-2 Math XL

LESSON 1-3

Midpoint and Distance

The Midpoint Formula is used to find the midpoint of a segment in the coordinate plane and the Distance Formula is used to find the length. The Midpoint Formula can be adapted to partition a segment into any ratio of lengths.

Help Videos:

● How Do You Find the Midpoint Between Two Coordinates?

● How Was the Distance Formula Derived?

Practice:

1-3 Math XL

LESSON 1-4

Inductive Reasoning

Inductive reasoning can be used to identify patterns, provide evidence for or disprove conjectures, and make predictions.

Help Videos:

● What Is Inductive Reasoning?

● What Is a Counterexample?

Practice:

1-4 Math XL

LESSON 1-5

Conditional Statements

In mathematics, conditional statements are expressed as if-then statements consisting of a hypothesis and a conclusion. Conditional statements can be evaluated using truth tables.

Help Videos:

● How Do You Write the Converse, Inverse, and Contrapositive of a Conditional Statement and Determine Their Truth Values?

● How Do You Identify the Hypothesis and Conclusion of a Conditional Statement in If-Then Format?

Practice:

1-5 Math XL