1. Geometry Review Morgan Parsons Honors Geometry Mrs. Lowe June 2, 2009

2.  Formulas: Square A= S² P = 4s Triangle P = a + b + c A = ½ bh a b c Rectangle P = 2L + 2w A= Lw w L Circle C = 2 r A = r² Tips for Next years students: know your formulas! Knowing the formulas makes things easier as your geometry gets harder.

3. Chapter 3 -Parallel lines are two lines that are coplanar and do not intersect. -Perpendicular lines are two lines that intersect to form a right angle Corresponding Angles Postulate If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 1 2 Example:  1   2

4. Chapter 4 Two figures are congruent if they have exactly the same size and shape. SSS Congruence Postulate – If 3 sides of one triangle are congruent to the three sides of a second triangle, then the two triangles are congruent. SAS Congruence Postulate – If 2 sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. ASA Congruence Postulate – If 2 angles & the included side of one triangle are congruent to 2 angles & the included side of a second triangle, then the 2 triangles are congruent. AAS Congruence Theorem – If 2 angles & a non-included side of one triangle are congruent to 2 angles & the corresponding non-included side of a second triangle, then the two triangles are congruent.

5. Chapter 6 1 2 3 4 Theorem 6.1 Interior Angles of a Quadrilateral The sum of the measures of the interior angles of a quadrilateral is 360  m  1 + m  2 + m  3 + m  4 = 360  Corollaries About Special Quadrilaterals Rhombus Corollary A quadrilateral is a rhombus if and only if it has four congruent sides. Rectangle Corollary A quadrilateral is a rectangle if and only if it has four right angles. Square Corollary A quadrilateral is a square if and only if it is a rhombus and a rectangle.

6. Chapter 7 Reflection – Where the line acts like a mirros, with an image reflected in the line. Rotation – Transformation in which a figure is turned around a fixed point. Translation - a transformation that maps every two points P and Q in the plane to points P’ and Q’, so that the following properties are true. 1. PP’ = QQ’ 2. PP’ || QQ’, or PP’ and QQ’ are collinear. P’ Q’ P Q

7. Chapter 8 When there is a correspondence between two polygons such that their corresponding angles are congruent and the lengths of corresponding sides are proportional the two polygons are called similar polygons. AA Similarity Postulate If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. SSS Similarity Theorem If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar. SAS Similarity Theorem If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides are proportional then the triangles are similar.

8. Chapter 9 Right triangles whose angle measures are 45  -45  -90  or 30  -60  -90  are called special right triangles. 45  -45  -90  Triangle Theorem In a 45  -45  -90  triangle, the hypotenuse is  2 times as long as each leg. 45  x x  2x Hypotenuse =  2  leg 30  -60  -90  Triangle Theorem In a 30  -60  -90  triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is  3 times as the shorter leg. 60  30  x 3x3x 2x Hypotenuse = 2  shorter leg Longer leg =  3  shorter leg

9. Chapter 10 Center Diameter Radius chord Secant

10. Chapter 11 Circumference of a circle = 2  r Arc Length Corollary In a circle, the ratio of the length of a given arc to the circumference is equal to the ratio of the measure of the arc to 360  Arc length of AB 2  r = mAB 360  Area of a circle =  r 2 Area of a Sector The ratio of the area A of a sector of a circle to the area of a circle is equal to the ratio of the measure of the intercepted arc to 360  A mAB  r 360  = 2

11. Chapter 12 Volume Postulates Postulate 27 Volume of a cube The volume of a cube is the cube of the length of its side, or v = s³ Postulate 28 Volume Congruence Postulate If two polyhedra are congruent, then they have the same volume. Postulate 29 Volume Addition Postulate The volume of a solid is the sum of the volumes of all its non-overlapping parts. Euler’s Theorem The number of faces (F), vertices (V), and edged (E) of a polyhedron are related by the formula F + V = E = 2.

12. THE END :)