Study Guide

Vocabulary

Acute Angle – any angle less than 90º

a 90º angle Right Angle –

any angle larger than 90º Obtuse Angle -

angles that add up to 90º Complementary Angles –

angles that add up to 180º Supplementary Angles –

Adjacent Angles - angles that share a common vertex and ray…angles that are back to back. *Vertex – the “corner” of the angle *Ray – a line that has an endpoint on one end and goes on forever in the other direction.

A ≅ B denotes that A is congruent to B. Congruent Angles – Angles with equal measurement A ≅ B denotes that A is congruent to B.

a line that intersects a set of parallel lines Transversal - a line that intersects a set of parallel lines t

Vertical Angles Two angles that are opposite angles at intersecting lines. Vertical angles are congruent angles. t 1   4 2   3 1 2 3 4

1   5 2   6 3   7 4   8 Corresponding Angles Two angles that occupy corresponding positions when parallel lines are intersected by a transversal…same side of transversal AND same side of own parallel line. Corresponding angles are congruent angles. t 1   5 2   6 3   7 4   8 Top Left Top Right 1 2 3 4 5 6 7 8 Bottom Left Bottom Right Top Left Top Right Bottom Left Bottom Right

1+2=180 2+4=180 4+3=180 3+1=180 5+6=180 6+8=180 8+7=180 Linear Pair Two adjacent angles that form a line. They are supplementary. (angle sum = 180) 1 2 3 4 5 6 7 8 t 1+2=180 2+4=180 4+3=180 3+1=180 5+6=180 6+8=180 8+7=180 7+5=180

Alternate Exterior Angles Two angles that lie outside parallel lines on opposite sides of the transversal. They are congruent. t 2   7 1   8 1 2 3 4 5 6 7 8

Alternate Interior Angles Two angles that lie between parallel lines on opposite sides of the transversal. These angles are congruent. t 3   6 4   5 1 2 3 4 5 6 7 8

Same Side Interior Angles Two angles that lie between parallel lines on the same sides of the transversal. These angles are supplementary. t 3 +5 = 180 4 +6 = 180 1 2 3 4 5 6 7 8 *Also known as Consecutive Interior Angles

Same Side Exterior Angles Two angles that lie outside parallel lines on the same side of the transversal. These angles are supplementary. t 1 +  7 = 180 2 +  8 = 180 1 2 3 4 5 6 7 8 *Also known as Consecutive Exterior Angles

Proportions: Two fractions that are set up equal to each other Proportions: Two fractions that are set up equal to each other. To solve for a missing part of a proportion, cross multiply, then solve the equation. Ratio: Comparing quantities: Can be written as a fraction, with the word to in between the numbers or with a : in between the numbers. Scale factor is what you multiply the pre-image (original figure) by in order to get the image (new figure). The scale factor of the perimeter squared IS the scale factor of the area of two figures.

Similar Figures: Corresponding angles have the same measurement AND corresponding sides are proportional. Unit Rate: A ratio with a denominator of one. (The cost of one notebook, etc)

Word Problems 1. Set up a proportion by labeling the numerators and the denominators. 2. Then place the numbers in the correct places BEING CAREFUL TO READ THE LABELS YOU CREATED. 3. Cross multiply. 4. Solve the equation.

Triangles – all angles add up to 180º How do we classify triangles based on its sides?

How do we classify triangles based on its angles? Equilateral or

Quadrilaterals – a four sided figure.

Perimeter – the distance around a figure Perimeter – the distance around a figure. (Add up all sides of the figure.)

Circumference – the distance around a circle Circumference – the distance around a circle. Diameter – the distance across a circle making certain to go through the center. Radius – the distance from any point on a circle to the center.

Triangular prism Rectangular prism Pentagonal prism

Cross section – the polygon (flat shape) that you see when you slice open a 3d figure.