3rd Quarter Math Reviewer PDF

3RD QUARTER MATH REVIEWER PARALLELOGRAMS Parallelograms-special type of quadrilaterals wherein their opposite sides are parallel. Intersecting Lines- Intersecting lines are two coplanar lines that have a common point. Concurrent Lines- three or more coplanar lines that share the same point. Perpend...

3RD QUARTER MATH REVIEWER PARALLELOGRAMS Parallelograms-special type of quadrilaterals wherein their opposite sides are parallel. Intersecting Lines- Intersecting lines are two coplanar lines that have a common point. Concurrent Lines- three or more coplanar lines that share the same point. Perpendicular lines- special intersecting lines wherein two coplanar lines intersect to form a right angle. Transversal lines- pass through two lines in the same plane at two distinct points. PROPERTIES OF PARALLELOGRAM 1.​ Opposite sides are parallel and congruent 2.​ Opposite angles are congruent 3.​ Consecutive angles are supplementary 4.​ Diagonals bisect each other 5.​ Each diagonals separate the parallelograms into two congruent triangles CONDITIONS FOR A QUADRILATERAL TO BE A PARALLELOGRAM REMEMBER The following conditions to consider for a quadrilateral to be a parallelogram: 1. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. 2. If a pair of opposite sides of a quadrilateral is congruent and parallel, then the quadrilateral is a parallelogram. 3. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. 4. If the consecutive angles of a quadrilateral is supplementary, then the quadrilateral is a parallelogram. 5. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. 6. If each diagonals of a quadrilateral form two congruent triangles, then the quadrilateral is a parallelogram. RECTANGLE -Parallelogram with 4 right angles. Equiangular but not equilateral. Properties of a Rectangle: 1.​ Opposite sides are parallel and congruent. 1.​ All angles are congruent. All angles are right. 2.​ Opposite angles are congruent and supplementary. 3.​ Consecutive angles are supplementary and congruent. 4.​ The diagonals bisect each other and congruent. 5.​ Each diagonal divides the rectangle into two congruent triangles. RHOMBUS -4 congruent sides. Equiangular but not equilateral. Properties of a Rhombus: 1.​ Opposite sides are parallel and congruent. 2.​ All sides are congruent. 3.​ Opposite angles are congruent. 4.​ Consecutive angles are supplementary. 5.​ Each diagonal bisects a pair of opposite angles. 6.​ Each diagonal is a perpendicular bisector of the other diagonal. 7.​ Each diagonal divides the rhombus into two congruent triangles. SQUARE -4 congruent sides and angles. Equiangular and equilateral. Both rhombus and rectangle. Properties of a Square: 1.​ All sides are parallel and congruent. 2.​ All angles are congruent. All angles are right. 3.​ Opposite angles are congruent and supplementary. 4.​ Consecutive angles are supplementary and congruent. 5.​ Diagonals are congruent and bisect opposite angles. 6.​ Each diagonal is a perpendicular bisector of the other diagonal. 7.​ 7.Each diagonal divides the square into two congruent triangles. Trapezoid -quadrilateral in which one and only one pair of opposite sides are parallel. Properties of trapezoid 1. Median is half the sum of the bases (Midsegment Theorem) 2. The legs of an isosceles trapezoid are congruent. 3. The base angles of an isosceles trapezoid are congruent. 4. The diagonals of an isosceles trapezoid are congruent. 5. Opposite angles of an isosceles trapezoid are supplementary. Median of a trapezoid is a segment which joins midpoints of the momparallel sides (legs). It is parallel to the bases and has a length equal to one-half of the sum of the lengths of the bases M= A+B 2 Isosceles trapezoid Legs are congruent Base angles are congruent Diagonals are congruent Properties of trapezoid Kite - a quadrilateral with reflection symmetry across one of its diagonals. Properties of kite 1. Two distinct pairs of consecutive sides are congruent. 2. One of the diagonals (longer diagonal) is a bisector of the other diagonal (shorter diagonal). 3. Only one pair of opposite angles is congruent. (at the end of the shorter diagonal) 4. One of the diagonals (longer diagonal) bisects the opposite angles of the kite. 5. The diagonals are perpendicular to each other. 6. The area of a kite is half the product of the lengths of its diagonals. Ratio and Proportion Ratio: A comparison of two quantities. It can be expressed in a:b colon form 𝑎/𝑏 fraction form a÷b division form a is to b phrase form Proportions A proportion is an equality of two ratios. a=c b d SIMILAR FIGURES -same shape -corresponding sides are proportional -corresponding angles are congruent CONGRUENT FIGURES -corresponding angles are congruent