Unit 2 Study Guide Topics: Transformations (Activity 9) o Translations o Rotations o Reflections. o Combinations of Transformations
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1 Geometry Name Unit 2 Study Guide Topics: Transformations (Activity 9) o Translations o Rotations o Reflections You are allowed a 3 o Combinations of Transformations inch by 5 inch Congruent Polygons (Activities 10 & 11) notecard o Using Transformations NO EXAMPLES o Proving Triangles congruent (SSS, SAS, ASA, AAS, HL) Flow Chart/Proofs (Activity 12) Triangle Properties (Activity 13) o Triangle Sum Theorem (all three angles in a triangle add up to 180 ) o Isosceles Triangles Midsegment of triangles Quadrilaterals (Activities 15 & 16) o Properties of Kites, trapezoids, parallelograms, rectangles, rhombi, and squares o Proving the name of a quadrilateral on the coordinate plane I. Transformations 1. Write the transformation in function notation. a. right 7 down 3 b. up 4 left 5 c. rotation of 90 counterclockwise d. reflection over the x-axis 2. Perform the indicated transformations. a. (x, y) (x + 4, y 6) b. (x, y) (x, y 8)
2 c. Reflection across the y axis d. Rotation Perform the following composition of transformations. a. T (5, 1) (R O, 90 ) b. R O,90 (T (0,7) ) II. Congruence 4. Given ABCD DEFA, find the following values. C 5 ft D a. m B = b. m EDA = B 100 E c. EF 25 7 ft d. AF = A F
3 5. State the triangle congruence condition, if any, that is the most direct way to show the triangles are congruent. (Use SSS, SAS, ASA, AAS, or HL. If the triangles are not congruent, write none.) a. b. c. 6. Point C is the center of the circle. Which triangle congruence criterion can be used to prove that the triangles are congruent? (Choose one) A. ASA B. SAS C. AAS D. SSS C 7. Complete the proof. Given: KB bisects AKC KB AC Prove: KAC is isosceles. Statements 1. KB bisects AKC 2. AKB CKB KB AC 1. Given 3. Given Reasons 4. m ABK = m CBK = Definition of perpendicular lines Definition of congruency 6. KB KB 7. ABK CBK CPCTC 6. Reflexive Property 9. KAC is isosceles. 9. Definition of Isosceles Triangles
4 For 8-12, complete the flow-chart proof of the definition of isosceles triangles. B Given: ABC is an isosceles triangle with base AC. BD is the angle bisector of ABC Prove: A C ABC is an isosceles triangle with base AC. Given AB BC Reason 1 A D C BD is the angle bisector of ABC Given 8. Reason 1 9. Reason Reason Reason Reason 5 ABD CBD Reason 2 BD BD Reason 3 ABD CBD A C Reason 4 Reason 5 ANSWER BANK A. ASA F. CPCTC B. AAS G. Congruence is Reflexive C. SAS H. Definition of Bisect D. SSS I. Definition of Isosceles E. HL J. Definition of Perpendicular III. Triangle Properties 13. Find the value of x. a. b Find the value of x and m A. 64
5 15. Complete the following proof. Given: ABC Prove: m 1 + m 2 + m 3 = 180 Statements 1. Figure ABC is a triangle. 1. Reasons 2. Draw DA BC 2. There is exactly one line that passes through two points. 3. m 3 m 4 3. m 2 m 5 4. m 5 + m 1 + m 4 = Substitution 16. LMN is an isosceles triangle with vertex angle M. If m L = 5x + 25 and m N = 8x Find m M. 17. In the triangle to the right, E and G are midpoints of FH and DF. Find the lengths of each missing segment. F 13 cm E G 15 cm 18. In the triangle at the right, M and N are midpoints of the sides of the triangle. Find the following: D 40 cm H a. x = b. y = c. MP = d. MN = e. QR =
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Perimeter Circle (circumference) C = 2πr Square P = 4s Rectangle P = 2b + 2h Area Circle A = πr Triangle A = bh Rectangle/Parallelogram A = bh Rhombus/Kite A = d d Trapezoid A = b + b h A area a apothem
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