University:
College Entrance Preparation
Course:
ACT Preparation (Mathematics)
Academic year:

2021
Views:

455

Pages:

5
Author:

Tarime9wn

**Segment Length and Midpoints** **Practice and Problem Solving: A/B** 1. Use a straightedge and a compass to construct a segment of length AB + CD. [Image of a construction with segments AB and CD] 2. Use a straightedge and a compass to construct a segment of length AB + CD. [Image of a construction with segments AB and CD] Use the distance formula or Pythagorean Theorem to determine whether each pair of segments have the same length. Justify with work. 3. CD and EF CD = √17 ≈ 4.1 EF = √13 ≈ 3.6 **Not congruent** 4. GH and JK GH = √20 ≈ 4.5 JK = √17 ≈ 4.1 **Not congruent** Determine the coordinates of the midpoint or other endpoint for each segment. Identify the quadrant that each midpoint lies. 5. PQ has endpoints P(5, -3) and Q(2, 4). Midpoint: (3.5, 0.5) Quadrant: I 6. RS has endpoint R(-2, 3) and midpoint M(-5, 1/2). Endpoint: (-8, -2) Midpoint is in Quadrant II **a)** Find the value of x and the length of each segment. [Image of a line segment with points A, B, C, D, E] 13 + 6 + 2x - 18 = 4x - 29 2x + 1 = 4x - 29 30 = 2x x = 15 UV = 31 BC = 11 CD = 15 DE = 14 BE = 25 **b)** [Image of a line segment with points B, C, D, and E] 3x + 47 + y = 27 + x y + 10 = x + 16 y = x + 6 y = -2x + 20 x + 6 = -2x + 20 3x = 14 x = 14/3 **Lesson 1-2** **Angle Measures and Angle Bisectors** **Practice and Problem Solving: A/B** **Construct a copy of each angle. Then state the type of angle.** 1. [Image of an acute angle] Acute 2. [Image of an obtuse angle] Obtuse **Use a compass and a straightedge to construct the bisector of each angle. Then measure the angles to confirm it has been bisected. Record the angle measures.** 3. [Image of an angle bisector with angles measuring 40 degrees each] 4. [Image of an angle bisector with angles measuring 50 degrees each] 5. [Image of an angle bisector with angles measuring 20 degrees each] 6. Explain how you can use a straightedge and a protractor to show that each angle you formed by a bisector is one-half the original angle. Verify that the sum of the 2 smaller angle measures is equal to the half of the measure of the original angle. 7. Find the value of x. QR bisects ∠PQS. Find m∠PQR and m∠PQS. [Image of an angle with points P, Q, R, and S] 4x - 10 = x + 130 7x = 140 x = 20 ∠PQR = 70° ∠PQS = 140° 8. Find the value of x. Find m∠CAD and m∠BAD. [Image of an angle with points A, B, C, and D] 5x + 57 + x + 15 = 90 6x + 72 = 90 x = 3 ∠CAD = 18° ∠BAD = 72° 9. Find m∠RST m∠RSL = 91° Find m∠RST [Image of an angle with points R, S, T, and U] ∠RST = 22° **Representing and Describing Transformations** **Lesson 1-3** **Practice and Problem Solving: A/B** 1. Use coordinate notation to describe the transformation of ΔPQR. P(-4, 5) -> P'(2, 4) Q(-5, 2) -> Q'(1, 1) R(-1, 3) -> R'(5, 2) (x, y) -> (x + 6, y - 1) 2. Describe the algebraic rule for ΔDEF. (x, y) -> (3x, 3y) Name the transformation described by the given rule. 3. (x, y) -> (-x, y) Reflect across y-axis 4. (6, 2) -> (-6, -2) Rotate 180° about origin 5. (5, 8) -> (8, -5) Rotate 90° clockwise OR Rotate 270° counterclockwise 6. (x, y) -> (x + 9, y + 2) Translate (shift) right 9 and up 2