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More Lessons for Geometry

Common Core For Geometry

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΅πΆ and
π΄β²π΅β²πΆβ² so that π΄π΅ = π΄β²π΅β² (Side),
πβ π΄ = πβ π΄β² (Angle), and
π΄πΆ = π΄
β²πΆ
β²
(Side), then the triangles
are congruent.

[SAS]

Given two triangles π΄π΅πΆ and
π΄β²π΅β²πΆβ², if πβ π΄ = πβ π΄β² (Angle),
π΄π΅ = π΄β²π΅β² (Side), and πβ π΅ = πβ π΅β²
(Angle), then the triangles are
congruent.

[ASA]

Given two triangles π΄π΅πΆ and
π΄β²π΅β²πΆβ², if π΄π΅ = π΄β²π΅β² (Side),
π΄πΆ = π΄β²πΆβ² (Side), and π΅πΆ = π΅β²πΆβ²
(Side), then the triangles are
congruent.

[SSS]

Given two triangles π΄π΅πΆ and
π΄β²π΅β²πΆβ², if π΄π΅ = π΄β²π΅β² (Side),
πβ π΅ = πβ π΅β² (Angle), and
πβ πΆ = πβ πΆβ² (Angle), then the
triangles are congruent.

[AAS]

Given two right triangles π΄π΅πΆ and
π΄β²π΅β²πΆβ² with right angles β π΅ and β π΅β²,
if π΄π΅ = π΄β²π΅β² (Leg) and π΄πΆ = π΄β²πΆβ²
(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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