p. 33 - Frame 41

Pr.1 All right angles are congruent. Proof - Frame 47
Pr. 2 All straight angles are congruent. Proof - Self Test # 13
Pr. 3 Complements of same or congruent angles are congruent. Proof - Frame 47
Pr. 4 Supplements of same or congruent angles are congruent. Proof - Frame 48
Pr. 5 Vertical angles are congruent. Proof - Frame 49

 

p. 51 - Frame 2

Pr. 1 Corresponding parts of congruent triangles are congruent. Postulate - CPCTC
Pr. 2 Two triangles are congruent if 2 sides and included angle are congruent. Postulate - SAS
Pr. 3 Two triangles are congruent if 2 angles and included side are congruent. Postulate - ASA
Pr. 4 Two triangles are congruent if three sides are congruent. Postulate - SSS

 

p. 58 - Frame 7

Pr. 1 Base angles of an isosceles triangle are congruent. Proof - In class
Pr. 2 If two angles of a triangle are congruent, the sides opposite them are congruent. Proof - In class
Pr. 3 An equilateral triangle is equiangular. Proof - In class
Pr. 4 An equiangular triangle is equilateral. Proof - In class

 

p. 61 - Frame 10 - Theorem: The bisector of the vertex angle of an isosceles triangle is a median to the base.

 

p. 67 - Frame 12

Pr. 1 Through a given point not on a given line, one and only one line can be drawn parallel to the given line. Postulate (Parallel)
Pr. 2 Two lines are parallel if a pair of corresponding angles are congruent. Postulate
Pr. 3 Two lines are parallel if a pair of alternate interior angles are congruent. Proof - Student Exercise
Pr. 4 Two lines are parallel if a pair of interior angles on the same side of a transversal are supplementary. Proof - Student Exercise
Pr. 5 Lines are parallel if they are perpendicular to the same line. Proof - Student Exercise
Pr. 6 Lines are parallel if they are parallel to the same line. Proof - Student Exercise
Pr. 7 If two lines are parallel, each pair of corresponding angles are congruent. Postulate
Pr. 8 If two lines are parallel, each pair of alternate interior angles are congruent. Proof - Student Exercise
Pr. 9 If two lines are parallel, each pair of interior angles on the same side of the transversal are supplementary. Proof - Student Exercise
Pr. 10 If two lines are parallel, a line perpendicular to one of them is perpendicular to the other also. Proof - Student Exercise
Pr. 11 If lines are parallel, a line parallel to one of them is parallel to the others also. Proof - Student Exercise
Pr. 12 If the sides of two angles are respectively parallel to each other, the angles are either congruent or supplementary. Proof - Student Exercise

 

p. 71 - Frame 15

Pr. 1 If a point is on the perpendicular bisector of a line segment, then it is equidistant from the ends of the segment it bisects. Proof - In class
Pr. 2 If a point is equidistant from the ends of a line segment, then it is on the perpendicular bisector of the line segment. Proof - In class
Pr. 3 If a point is on the bisector of an angle, then it is equidistant from the sides of the angle. Proof - Student Exercise
Pr. 4 If a point is equidistant from the sides of an angle, then it is on the bisector of the angle. Proof - Student Exercise
Pr. 5 Two points each equidistant from the ends of a line segment determine the perpendicular bisector of the line segment. Proof - Student Exercise
Pr. 6 The perpendicular bisectors of the sides of a triangle meet in a point that is equidistant from the vertices of the triangle.
Circumcenter-center of circumscribed circle
Proof - Student Exercise
Pr. 7 The bisectors of the angles of a triangle meet in a point that is equidistant from the sides of the triangle.
Incenter-center of inscribed circle
Proof - Student Exercise

 

p. 76 - Frame 17

Pr. 1 The sum of the angles of a triangle equals 180°. Proof - In text
Pr. 2 If two angles of one triangle are congruent respectively to two angles of another triangle, the remaining angles are congruent. Proof - Student Exercise
Pr. 3 The sum of the values of the angles of a quadrilateral equals 360°. Proof - Student Exercise
Pr. 4 The value of each exterior angle of a triangle equals the sum of its two non-adjacent (opposite) interior angles. Proof - Student Exercise
Pr. 5 The sum of the exterior angles of a triangle equals 360°. Proof - Student Exercise
Pr. 6 Each angle of an equilateral triangle equals 60°. Proof - Student Exercise
Pr. 7 The acute angles of a right triangle are complementary. Proof - Student Exercise
Pr. 8 Each acute angle of an isosceles right triangle equals 45°. Proof - Student Exercise
Pr. 9 A triangle can have no more than one right angle. Proof - Student Exercise
Pr. 10 A triangle can have no more than one obtuse angle. Proof - Student Exercise
Pr. 11 Two angles are congruent or supplementary if their sides are respectively perpendicular to each other. Proof - Student Exercise

 

p. 81 - Frame 21

Pr. 1 If S is the sum of the interior angles of a polygon of n sides, then S = (n-2)180°. Proof - Text (partial)
Pr. 2 The sum of the exterior angles of any polygon equals 360°. Proof - In class
Pr. 3 A regular polygon of n sides has an exterior angle of 360°/n and an interior angle of 180°-360°/n. Proof - In class

 

p. 83 - Frame 23

Pr. 1 If two angles and a side opposite one of them of one triangle are congruent to the corresponding parts of another, the triangles are congruent. SAA or AAS
Proof - Student exercise
Pr. 2 If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, the triangles are congruent. HL
Proof - Not given

 

p. 91 - Frame 25

Pr. 1 The base angles of an isosceles trapezoid are congruent. Proof - Not given
Pr. 2 If the base angles of a trapezoid are congruent, the trapezoid is isosceles. Proof - Not given

 

p. 92 - Frames 27 & 28

Pr. 1 The opposite sides of a parallelogram are parallel. Definition
Pr. 2 A diagonal of a parallelogram divides it into two congruent triangles. Proof - In class
Pr. 3 The opposite sides of a parallelogram are congruent. Proof - Student Exercise
Pr. 4 The opposite angles of a parallelogram are congruent. Proof - Student Exercise
Pr. 5 Any two adjacent angles of a parallelogram are supplementary. Proof - Student Exercise
Pr. 6 The diagonals of a parallelogram bisect each other. Proof - Student Exercise
Pr. 7 A quadrilateral is a parallelogram if its opposite sides are parallel. Definition
Pr. 8 A quadrilateral is a parallelogram if its opposite sides are congruent. Proof - Student Exercise
Pr. 9 A quadrilateral is a parallelogram if two sides are congruent and parallel. Proof - Student Exercise
Pr. 10 A quadrilateral is a parallelogram if its opposite angles are congruent. Proof - Student Exercise
Pr. 11 A quadrilateral is a parallelogram if its diagonals bisect each other. Proof - Student Exercise

 

p. 98 - Frames 33 to 35

Pr. 1 A rectangle, rhombus, or square has all the properties of a parallelogram. Definition
Pr. 2 Each angle of a rectangle is a right angle. Proof - In class
Pr. 3 The diagonals of a rectangle are congruent. Proof - Student Exercise
Pr. 4 All sides of a rhombus are congruent. Proof - Student Exercise
Pr. 5 The diagonals of a rhombus are perpendicular bisectors of each other. Proof - Student Exercise
Pr. 6 The diagonals of a rhombus bisect the vertex angles. Proof - Student Exercise
Pr. 7 The diagonals of a rhombus form four congruent triangles. Proof - Student Exercise
Pr. 8 A square has all the properties of both the rhombus and the rectangle. Proof - In text
Pr. 9 If a parallelogram has one right angle, then it is a rectangle. Proof - Student Exercise
Pr. 10 If a parallelogram has congruent diagonals, then it is a rectangle. Proof - Student Exercise
Pr. 11 If a parallelogram has congruent adjacent sides, then it is a rhombus. Proof - Student Exercise
Pr. 12 If a parallelogram has a right angle and two equal adjacent sides, then it is a square. Proof - Student Exercise

 

p. 101 - Frame 36

Pr. 1 If three or more parallels cut off congruent segments on one transversal, then they cut off congruent segments on any other transversal. Proof - In class
Pr. 2 If a line is drawn from the midpoint of one side of a triangle and parallel to a second side, then it passes through the midpoint of the third side. Proof - Student Exercise
Pr. 3 If a line joins the midpoints of two sides of a triangle, then it is parallel to the third side and equal to one-half of it. Proof - Not given
Pr. 4 The median of a trapezoid is parallel to its bases and equal to one-half of their sum. Proof - Student Exercise
Pr. 5 The median to the hypotenuse of a right triangle equals one-half of the hypotenuse. Proof - Student Exercise
Pr. 6 The medians of a triangle meet in a point that is two-thirds of the distance from any vertex to the midpoint of the opposite side. Proof - Not given

 

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