Session 2 Draw six segments that pass through every dot in the figure without taking your pencil off the paper.

Warm-up: Using the Pythagorean Theorem Find the value of x. Give your answer in simplest radical form. a2 + b2 = c2 Pythagorean Theorem 22 + 62 = x2 Substitute 2 for a, 6 for b, and x for c. 40 = x2 Simplify. Find the positive square root. Simplify the radical.

Warmup #2: Using the Pythagorean Theorem Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain. a2 + b2 = c2 Pythagorean Theorem 42 + b2 = 122 Substitute 4 for a and 12 for c. b2 = 128 Multiply and subtract 16 from both sides. Find the positive square root.

Bonus: Using the Pythagorean Theorem Find the value of x. Give your answer in simplest radical form. a2 + b2 = c2 Pythagorean Theorem (x – 2)2 + 42 = x2 Substitute x – 2 for a, 4 for b, and x for c. x2 – 4x + 4 + 16 = x2 Multiply. –4x + 20 = 0 Combine like terms. 20 = 4x Add 4x to both sides. 5 = x Divide both sides by 4.

Homework Review The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then it’s Odd. If you get different y’s, then it’s Neither.

Geometry Vocabulary The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then it’s Odd. If you get different y’s, then it’s Neither.

Point An exact position or location in a given plane. Point A or Point B

Line The set of points between points A and B in a plane and the infinite number of points that continue beyond the points. Written as

Line Segment A line with two endpoints. Written as

Ray A line that starts at A, goes through B, and continues on. Written as

Plane A flat, two-dimensional surface that extends infinitely far.

Angle Formed by 2 rays coming together at a common point (Vertex) The angle is

Right Angle An angle that measures 90°.

Acute Angle An angle measuring less than 90° but greater than 0°.

Obtuse Angle An angle measuring greater than 90° but less than 180°.

Parallel Line Lines in a plane that either do not share any points and never intersect, or share all points. Written as

Perpendicular Line Two lines that intersect at a right angle (90°). Written as

Circle The set of points on a plane at a certain distance, or radius, from a single point, the center

Distance along a line The linear distance between two points on a given line.

How far apart are the points on the line segment?

How far apart are the points on the line segment? Hmmm…

CW Vocabulary Practice WS

Angle Addition Postulate If B lies on the interior of ÐAOC, then mÐAOB + mÐBOC = mÐAOC. B A mÐAOC = 115° 50° 65° C O

A B C D G K H J 134° 46° 46 Given: mÐGHK = 95 mÐGHJ = 114. Example 1: Example 2: G 114° K 46° 95° 19° H This is a special example, because the two adjacent angles together create a straight angle. Predict what mÐABD + mÐDBC equals. ÐABC is a straight angle, therefore mÐABC = 180. mÐABD + mÐDBC = mÐABC mÐABD + mÐDBC = 180 So, if mÐABD = 134, then mÐDBC = ______ J Given: mÐGHK = 95 mÐGHJ = 114. Find: mÐKHJ. The Angle Addition Postulate tells us: mÐGHK + mÐKHJ = mÐGHJ 95 + mÐKHJ = 114 mÐKHJ = 19. Plug in what you know. 46 Solve.

Set up an equation using the Angle Addition Postulate. Given: mÐRSV = x + 5 mÐVST = 3x - 9 mÐRST = 68 Find x. Algebra Connection R V Extension: Now that you know x = 18, find mÐRSV and mÐVST. mÐRSV = x + 5 mÐRSV = 18 + 5 = 23 mÐVST = 3x - 9 mÐVST = 3(18) – 9 = 45 Check: mÐRSV + mÐVST = mÐRST 23 + 45 = 68 S T Set up an equation using the Angle Addition Postulate. mÐRSV + mÐVST = mÐRST x + 5 + 3x – 9 = 68 4x- 4 = 68 4x = 72 x = 18 Plug in what you know. Solve.

x – 7 + 2x – 1 = 2x + 34 3x – 8 = 2x + 34 x – 8 = 34 x = 42 x = 42 C B mÐBQC = x – 7 mÐCQD = 2x – 1 mÐBQD = 2x + 34 Find x, mÐBQC, mÐCQD, mÐBQD. C B mÐBQC = x – 7 mÐBQC = 42 – 7 = 35 mÐCQD = 2x – 1 mÐCQD = 2(42) – 1 = 83 mÐBQD = 2x + 34 mÐBQD = 2(42) + 34 = 118 Check: mÐBQC + mÐCQD = mÐBQD 35 + 83 = 118 Q D mÐBQC + mÐCQD = mÐBQD x – 7 + 2x – 1 = 2x + 34 3x – 8 = 2x + 34 x – 8 = 34 x = 42 x = 42 mÐBQC = 35 mÐCQD = 83 mÐBQD = 118 Algebra Connection Slide 5

HW Angle Addition Postulate WS