Lines, Angles, and Triangles Geometry Topic 2 Lines, Angles, and Triangles

Table of Contents Recommended Instructional Design and Planning Continuum ........Slide 3 Vocabulary …………………………………………………………………….……………..Slides 4 – 22 Reporting Category Practice Items ………………….…………………………….Slides 23 - 51

Vocabulary

Mathematically Speaking! Choose 3-4 vocabulary words for the day. Throughout the lesson, as students respond to your questions or are presenting a problem on the board, mark a tally when a vocabulary word is used accurately. This can be turned into a competition among groups or between periods. Examples of accuracy vertical angles vs opposite angles hypotenuse vs the long side congruent vs same

Vertical angles – the non adjacent angles formed by two intersecting lines. ∠1 and ∠3 are vertical angles. ∠2 and ∠4 are vertical angles.

Transversal – a line that intersects at least two other lines. Line 𝑡 is a transversal.

Parallel Lines

Indirect proof – a proof in which the statement to be proved is assumed to be false and a contradiction is shown.

Hypotenuse – the side opposite the right angle in a right triangle.

Interior angle – an angle formed by two sides of a polygon with a common vertex.

Auxiliary line – a line drawn in a figure to aid in a proof.

Exterior angle – an angle formed by one side of a polygon and the extension of an adjacent side.

Isosceles triangle – a triangle with at least two congruent sides.

Equilateral triangle – a triangle with three congruent sides. Equiangular triangle – a triangle with three congruent angles.

Triangle Inequality Theorem - The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Example: AB + BC > AC AC + BC > AB AB + AC > BC

Congruent Triangles Two possible congruence statements: ∠ABC ≅ ∠FED ∠BCA ≅ ∠EDF

SSS Triangle Congruence Postulate

SAS Triangle Congruence Postulate

ASA Triangle Congruence Postulate

AAS Triangle Congruence Theorem

HL Right Triangle Congruence