# Review of the Assumptions (Axioms)

### New York State Common Core Math Geometry, Module 1, Lesson 34

Worksheets for Geometry, Module 1, Lesson 34

Student Outcomes

• Students examine the basic geometric assumptions from which all other facts can be derived.
• Students review the principles addressed in Module 1.

Review of the Assumptions (Axioms)

Classwork

Review Exercises

Given two triangles π΄π΅πΆ and π΄β²π΅β²πΆβ² so that π΄π΅ = π΄β²π΅β² (Side), πβ π΄ = πβ π΄β² (Angle), and π΄πΆ = π΄ β²πΆ β² (Side), then the triangles are congruent.
[SAS]

Given two triangles π΄π΅πΆ and π΄β²π΅β²πΆβ², if πβ π΄ = πβ π΄β² (Angle), π΄π΅ = π΄β²π΅β² (Side), and πβ π΅ = πβ π΅β² (Angle), then the triangles are congruent.
[ASA]

Given two triangles π΄π΅πΆ and π΄β²π΅β²πΆβ², if π΄π΅ = π΄β²π΅β² (Side), π΄πΆ = π΄β²πΆβ² (Side), and π΅πΆ = π΅β²πΆβ² (Side), then the triangles are congruent.
[SSS]

Given two triangles π΄π΅πΆ and π΄β²π΅β²πΆβ², if π΄π΅ = π΄β²π΅β² (Side), πβ π΅ = πβ π΅β² (Angle), and πβ πΆ = πβ πΆβ² (Angle), then the triangles are congruent.
[AAS]

Given two right triangles π΄π΅πΆ and π΄β²π΅β²πΆβ² with right angles β π΅ and β π΅β², if π΄π΅ = π΄β²π΅β² (Leg) and π΄πΆ = π΄β²πΆβ² (Hypotenuse), then the triangles are congruent.
[HL]

The opposite sides of a parallelogram are congruent.
The opposite angles of a parallelogram are congruent.
The diagonals of a parallelogram bisect each other.

The midsegment of a triangle is a line segment that connects the midpoints of two sides of a triangle; the midsegment is parallel to the third side of the triangle and is half the length of the third side.

The three medians of a triangle are concurrent at the centroid; the centroid divides each median into two parts, from vertex to centroid and centroid to midpoint, in a ratio of 2:1.

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