Conjecture- unproven statement that is based on observations. Inductive reasoning- looking for patterns and making conjectures is part of this process.

Conjecture- unproven statement that is based on observations. Inductive reasoning- looking for patterns and making conjectures is part of this process Counterexample- example shows a conjecture is false. Point- no dimensions. Line- extends in one dimension. Plane- extends in two directions. Collinear points- points that lie on the same line. Coplanar points- points that lie on the same plane. Acute angles- less than 90 degrees Right angles- equal to 90 degrees Obtuse angles- more than 90 degrees Straight angles- equal to 180 degrees Complementary angles- sum of measures is 90 degrees. Supplementary angles- sum of measures is 180 degrees. Distance Formula- AB=Square root of(x-x1)+(y2-y1) Pythagorean Theorem- a+b=c Parallel lines- coplanar and do not intersect. Transversal- a line that intersects two or more coplanar lines at different points. Corresponding angles- if they occupy corresponding positions. Alternate exterior angles- if they lie outside the two lines on opposite sides of the transversal. Alternate interior angles- if they lie between the two lines on opposite sides of the transversal. Consecutive interior angles- if they lie between the two lines on the same side of the transversal. Theorem 3.1 If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. Theorem 3.2 If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. Theorem 3.3 If two lines are perpendicular, then they intersect to form four right angles. Theorem 3.4- Alternate Interior Angles If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Theorem 3.5- Consecutive Interior Angles If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. Theorem 3.6- Alternate Exterior Angles If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. Vertex - each of the three points joining the sides of a triangle. Adjacent sides- two sides sharing a common vertex. Hypotenuse- side opposite of the right angle. Congruent- correspondence between their angles and sides. Names of Triangles Equilateral Isosceles Scalene Classification by angles Acute Equiangular Right Obtuse Reflexive Property Every triangle is congruent to itself. Symmetric Property If triangle ABC is congruent to triangle DEF, the triangle DEF is congruent to triangle ABC. Transitive Property If triangle ABC is congruent to triangle DEF and triangle DEF is congruent to triangle JKL, then triangle ABC is congruent to triangle JKL. Side- Side-Side Side-Angle-Side Angle-Side-Angle Angle-Angle-Side Convex- if no line that contains a side of the polygon contains a point in the interior of the polygon. Concave- a polygon that is not convex. Diagonal- a segment that joins two nonconsecutive vertices. Theorem 6.6 If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Theorem 6.7 If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Theorem 6.8 If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram. Preimage- original figure. Image- new figure Transformation- operation that moves the preimage to the image. Translation- a transformation that maps every two points. Theorem 7.2 Rotation Theorem A rotation is an isometry. Theorem 7.3 If lines k and m intersect at point P, then a reflection in k followed by a reflection in m is a rotation about point P. Proportion- an equation that equates two ratios. Geometric mean- two positive numbers a and b is the positive number x such that a/x=x/b. Similar polygons- when there is a correspondence between two polygons such that their corresponding angles are congruent and the lengths of corresponding sides are proportional. Side-Side-Side If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar. Side-Angle-Side If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar. Special right triangles- have measures of or Sin, cosine, tangent- three basic trigonometric ratios. Trigonometric ratio- ratio of the lengths of two sides of a right triangle. Theorem Triangle In a triangle, the hypotenuse is square root of 2 times as long as each leg. Theorem Triangle In a triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is square root of 3 times as long as the shorter leg. Diameter- distance across the circle. Radius- distance from center to point on the circle. Chord- segment whose endpoints are points on the circle. Secant- a line that intersects a circle in two points. Tangent- a line in the plane of a circle that intersects the circle in exactly one point. Minor arc- part of a circle that measures less than 180 degrees. Major arc- part of a circle that measures between 180 degrees and 360 degrees. Semicircle- if the endpoints of an arc are the endpoints of diameter, then it is a semicircle. Theorem 10.1 If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. Theorem 10.2 In a plane, if a line is perpendicular to a radius if a circle at its endpoint on the circle, then the line is tangent to the circle. Circumference- is the distance around the circle. Arc length- portion of the circumference of a circle. Semicircle- one half of the circumference. To find the sum of the measures of interior angles of a polygon- 180 multiplied by the number of sides. Given that the radius of the circle is 5 cm, calculate the area of the shaded sector. (Take = 3.142). Area of Sector= =13.09cm Finding Arc Length Or you can use this step: Theorem 11.4 Area of Regular Polygons The area of a regular n-gon with side length s is half the product of the apothem a and the perimeter P, so A=(1/2)aP or A=(1/2)aXns. Theorem 11.8 The ratio of the area A of a sector of a circle to the area of the circle is equal to the ratio of the measure of the intercepted arc to 360 degrees. Faces- a solid that is bounded by polygons. Edge- line segment formed by the intersection of two faces. Vertex- point where three or more edges meet.