Geometry Notes - Angle Pairs & Midpoint/Distance Formulas PDF

Notes 1.6: Angle pairs Learning target: apply algebra techniques to classify angle relationships Learning target: apply algebra techniques to classify angle relationships adjacent angles— vertex— Learning target: apply algebra techniques to classify...

Notes 1.6: Angle pairs Learning target: apply algebra techniques to classify angle relationships Learning target: apply algebra techniques to classify angle relationships adjacent angles— vertex— Learning target: apply algebra techniques to classify angle relationships vertical angles— Learning target: apply algebra techniques to classify angle relationships linear pair—  Learning target: apply algebra techniques to classify angle relationships complimentary angles—  Learning target: apply algebra techniques to classify angle relationships supplementary—  Learning target: apply algebra techniques to classify angle relationships Use the figure to answer each statement as true or false. a. ∠2 and ∠3 are vertical angles. b. ∠2 and ∠4 are vertical angles  Learning target: apply algebra techniques to classify angle relationships Use the figure to answer each statement as true or false. c. ∠3 and ∠4 form a linear pair. d. ∠3 and ∠1 form a linear pair.  Learning target: apply algebra techniques to classify angle relationships Use the figure to identify each pair of complementary angles.  Learning target: apply algebra techniques to classify angle relationships Use the figure to identify each pair of supplementary angles. Learning target: apply algebra techniques to classify angle relationships Given that m∠P = 73°: a. If ∠A and ∠P are supplementary angles, find m∠A. b. If ∠B and ∠P are complementary angles, find m∠B.  Learning target: apply algebra techniques to classify angle relationships angle bisector—  Learning target: apply algebra techniques to classify angle relationships Use the figure shown to find the measure of each unknown angle. a. Find m∠BAC. b. Find m∠BAE.  Learning target: apply algebra techniques to classify angle relationships In the figure, ray QY bisects ∠RQZ. Find the value of x; then find m∠RQY and m∠YQZ.  Learning target: apply algebra techniques to classify angle relationships Solve for x and y. Then find the measure of each angle.  Notes 1.7: Midpoint and distance formulas Learning target: apply the midpoint and distance formulas to calculate geometric measures  Learning target: apply the midpoint and distance formulas to calculate geometric measures From previous sections in this chapter, we know the definition of the term “midpoint”. Write your definition below. Check with the person next to you.  Learning target: apply the midpoint and distance formulas to calculate geometric measures Midpoint Formulas On a Number Line The coordinate of the midpoint is the average or mean of the coordinates of the endpoints. Formula Given on a number line: The coordinate of the midpoint M of is  Learning target: apply the midpoint and distance formulas to calculate geometric measures On the Coordinate Plane The coordinates of the midpoint are the average of the x-coordinates and the average of the y-coordinates of the endpoints. Learning target: apply the midpoint and distance formulas to calculate geometric measures Use the diagram and find the coordinate of the midpoint, M, of segment PQ. Learning target: apply the midpoint and distance formulas to calculate geometric measures Find the midpoint of the line segment PQ, that joins points P(–3, 3) and Q(1, 0).  Learning target: apply the midpoint and distance formulas to calculate geometric measures The midpoint of segment CD is M(–2, 1). One endpoint is C(–5, 7). What are the coordinates of the other endpoint, D?  Learning target: apply the midpoint and distance formulas to calculate geometric measures The distance between two points A(x1, y1) and B(x2, y2) is The Distance Formula is based on the Pythagorean Theorem, which we will study later in this book. When we use the Distance Formula, we are really finding the length of the hypotenuse of a right triangle. Learning target: apply the midpoint and distance formulas to calculate geometric measures  Learning target: apply the midpoint and distance formulas to calculate geometric measures Find the distance between A(2, –5) and B(1, –4). Give an exact distance and a one-decimal-place approximation. 1.4 Extended Notes 𝐿 1. In the figure, line 𝑡 bisects 𝐽𝐿̅ at point K. If 𝐽𝐾 = 2𝑥 + 2, 𝐾𝐿 = 3𝑦 + 3, and 𝐽𝐿 = 4𝑥 + 𝑦 + 1, what are the values of 𝑥 and 𝑦? What are the lengths of ̅̅̅ ̅̅̅̅, and 𝐽𝐿 𝐽𝐾 , 𝐾𝐿 ̅? 𝑡 𝐾 𝐽 ̅̅̅̅. If 2. In the figure, 𝑆 is the midpoint of 𝑅𝑇 𝑅 2 𝑅𝑆 = 2𝑥 and 𝑆𝑇 = 7𝑥 + 4, then what is the value of 𝑥? What are the lengths of 𝑅𝑆 ̅̅̅̅, 𝑆𝑇 ̅̅̅̅, ̅̅̅̅? and 𝑅𝑇 𝑆 𝑇 1.5 Extended Notes 1. In the figure, 𝑚∠𝐽𝑂𝐿 = 2𝑥 2 − 𝑥 + 15 and 𝑚∠𝐿𝑂𝐾 = 5𝑥 + 5, what is the value of 𝑥? 𝐿 𝐽 𝑂 𝐾 𝐴 ⃑⃑⃑⃑⃑ bisects ∠𝐴𝐵𝐶. If 𝑚∠𝐴𝐵𝑋 = 6𝑥 + 2, 2. In the figure, 𝐵𝑋 𝑋 𝑚∠𝑋𝐵𝐶 = 5𝑦 + 2 and 𝑚∠𝐴𝐵𝐶 = 8𝑥 + 4𝑦, then what are the values of 𝑥 and 𝑦? 𝐵 𝐶 1.6 Extended Notes 1. The measure of the supplement of an is 14 less than three times the measure of the complement. Find the measure of the , its compliment, and its supplement. 2. Find 𝑥 and 𝑦 in the following figure. 3x 39 2 x 3 y 68 2 y 60 1.7 Extended Notes ̅̅̅̅. 1. Find the coordinates of the missing point given that M is the midpoint of 𝐴𝐵 7 12 𝐴 (√40, 8) , 𝑀(√160, 8 ) 2. The length of 𝐴𝐵 = √29, where pt. A has the coordinates (4, −1) and the coordinates of pt. B are (−1, 𝑘). Find 𝑘. (**HINT** There are 2 possible values for 𝑘) 1 Find the area of the shaded region. Assume all angles are right angles. Round your answers to the nearest tenth. 9 cm 3 cm 12 cm 8 cm 4 cm 2 cm 8 cm 9 cm 19 cm 2. The area of the rectangle below is 30 ft 2 , find x. 2x – 1 x+3 3. Find the EXACT perimeter of the triangle with the following coordinates of the vertices. J 3,5 , K 2,5 , L 2, 3 4. Find the perimeter of the following rectangle below. 3x 4 2x 2 y 1 2y 3