Review of the Assumptions (Axioms)

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 𝐴𝐵𝐶 and 𝐴′𝐵′𝐶′ so that 𝐴𝐵 = 𝐴′𝐵′ (Side), 𝑚∠𝐴 = 𝑚∠𝐴′ (Angle), and 𝐴𝐶 = 𝐴 ′𝐶 ′ (Side), then the triangles are congruent.
[SAS]

Given two triangles 𝐴𝐵𝐶 and 𝐴′𝐵′𝐶′, if 𝑚∠𝐴 = 𝑚∠𝐴′ (Angle), 𝐴𝐵 = 𝐴′𝐵′ (Side), and 𝑚∠𝐵 = 𝑚∠𝐵′ (Angle), then the triangles are congruent.
[ASA]

• Show Video for Whole Lesson

Given two triangles 𝐴𝐵𝐶 and 𝐴′𝐵′𝐶′, if 𝐴𝐵 = 𝐴′𝐵′ (Side), 𝐴𝐶 = 𝐴′𝐶′ (Side), and 𝐵𝐶 = 𝐵′𝐶′ (Side), then the triangles are congruent.
[SSS]

Given two triangles 𝐴𝐵𝐶 and 𝐴′𝐵′𝐶′, if 𝐴𝐵 = 𝐴′𝐵′ (Side), 𝑚∠𝐵 = 𝑚∠𝐵′ (Angle), and 𝑚∠𝐶 = 𝑚∠𝐶′ (Angle), then the triangles are congruent.
[AAS]

Given two right triangles 𝐴𝐵𝐶 and 𝐴′𝐵′𝐶′ with right angles ∠𝐵 and ∠𝐵′, if 𝐴𝐵 = 𝐴′𝐵′ (Leg) and 𝐴𝐶 = 𝐴′𝐶′ (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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