Review of the Assumptions (Axioms)


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

Worksheets for Geometry

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 𝐴𝐡𝐢 and 𝐴′𝐡′𝐢′ so that 𝐴𝐡 = 𝐴′𝐡′ (Side), π‘šβˆ π΄ = π‘šβˆ π΄β€² (Angle), and 𝐴𝐢 = 𝐴 ′𝐢 β€² (Side), then the triangles are congruent.
[SAS]

Given two triangles 𝐴𝐡𝐢 and 𝐴′𝐡′𝐢′, if π‘šβˆ π΄ = π‘šβˆ π΄β€² (Angle), 𝐴𝐡 = 𝐴′𝐡′ (Side), and π‘šβˆ π΅ = π‘šβˆ π΅β€² (Angle), then the triangles are congruent.
[ASA]

Given two triangles 𝐴𝐡𝐢 and 𝐴′𝐡′𝐢′, if 𝐴𝐡 = 𝐴′𝐡′ (Side), 𝐴𝐢 = 𝐴′𝐢′ (Side), and 𝐡𝐢 = 𝐡′𝐢′ (Side), then the triangles are congruent.
[SSS]

Given two triangles 𝐴𝐡𝐢 and 𝐴′𝐡′𝐢′, if 𝐴𝐡 = 𝐴′𝐡′ (Side), π‘šβˆ π΅ = π‘šβˆ π΅β€² (Angle), and π‘šβˆ πΆ = π‘šβˆ πΆβ€² (Angle), then the triangles are congruent.
[AAS]




Given two right triangles 𝐴𝐡𝐢 and 𝐴′𝐡′𝐢′ with right angles ∠𝐡 and βˆ π΅β€², if 𝐴𝐡 = 𝐴′𝐡′ (Leg) and 𝐴𝐢 = 𝐴′𝐢′ (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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