Download Geometric Proofs

GeometricProofs(Part1).notebook
April 07, 2016
Geometric Proofs
Mar 22­10:44 AM
Review of all the THEOREMS in GEOMETRY that you know.
Angles
1. Two adjacent angles are complementary when the sum of their measures is 90o.
2. Two adjacent angles are supplementary when the sum of their measures is 180o.
3. Vertically opposite angles are congruent. (VOC)
4. Corresponding angles formed by parallel lines and a transversal are congruent. (corr. angles are )
5. Alternate interior angles formed by parallel lines and a transversal are congruent. (alt. int. angles are )
6. Alternate exterior angles formed by parallel lines and a transversal are congruent. (alt. ext. angles are )
7. If the corresponding angles are congruent, or the alternate interior angles are congruent, or the alternate exterior angles are congruent, then the two lines intersected by a transversal are parallel.
Mar 22­12:43 PM
1
GeometricProofs(Part1).notebook
April 07, 2016
Mar 11­9:39 AM
Triangles
1. The sum of the measures of the interior angles of a triangle is 180º (Triangle Sum Theorem)
2. An isosceles triangle has two congruent sides. 3. In an isosceles triangle, the angles opposite the congruent sides are congruent.
4. The axis of symmetry of an isosceles triangle is a median, a perpendicular bisector, an angle bisector & an altitude of the triangle. 5. An equilateral triangle has three congruent sides.
6. In an equilateral triangle, each angle measures 60º.
7. All three axes of symmetry of an equilateral triangle are the medians, perpendicular bisectors, angle bisectors & altitudes of the triangle.
8. In a right triangle, the side opposite a 30º angle is one­half the length of the hypotenuse.
9. In a right triangle, the square of the hypotenuse is equal to the sum of the squares on the other two sides. (Pythagorean Theorem)
10. In any right triangle, the acute angles are complementary.
11. In any isosceles right triangle, each of the acute angles measures 45º
12. In any triangle, the measure of an exterior angle is equal to the sum of the two opposite interior angles
Mar 22­12:45 PM
2
GeometricProofs(Part1).notebook
April 07, 2016
Quadrilaterals
1. The sum of the measures of the interior angles of a quadrilateral is 360º.
Squares
1. A square has four congruent sides. 2. In a square, each angle measures 90º.
3. The diagonals of a square bisect each other perpendicularly.
Rhombuses
1. A rhombus has four congruent sides.
2. The diagonals of a rhombus are perpendicular to each other.
Rectangles
1. The opposite sides of a rectangle are congruent.
2. In a rectangle, each angle measures 90º.
3. The diagonals of a rectangle bisect each other.
Parallelograms
1. The opposite sides of a parallelogram are congruent.
2. The opposite angles of a parallelogram are congruent.
3. The consecutive angles of a parallelogram are supplementary.
4. The diagonals of a parallelogram bisect each other.
Mar 22­12:46 PM
Kites
1. A kite has two pairs of congruent sides.
2. The diagonals of a kite are perpendicular to each other.
Isosceles Trapezoids
1. An isosceles trapezoid has one pair of congruent sides.
2. A trapezoid has one pair of parallel sides.
Polygons
1. The sum of the interior angles of a convex polygon is o
(n­2) x 180 .
o
2. Each angle of a regular polygon is (n­2) x 180
2
Circles
1. In a circle, the measure of the radius is half the measure of the diameter.
2. All the diameters of a circle are congruent.
3. All the radii of a circle are congruent.
Mar 22­12:47 PM
3
GeometricProofs(Part1).notebook
April 07, 2016
Geometric Proofs
Example:
WB: p.190 #1a)
Justification
Statement
Apr 4­3:43 PM
WB: p.190 #1d)
Justification
Statement
Apr 6­11:12 AM
4
GeometricProofs(Part1).notebook
April 07, 2016
WB: p.191 #2
Statement
Justification
Mar 28­9:52 AM
Apr 11­10:09 AM
5
GeometricProofs(Part1).notebook
April 07, 2016
WB: p.192
Statement
Justification
Mar 28­10:11 AM
Statement
Justification
Apr 2­2:10 PM
6
GeometricProofs(Part1).notebook
April 07, 2016
Apr 9­10:59 AM
Apr 11­10:35 AM
7