z z Midterm #1 Chapters 13 Name ____________________________ Geometry Date _____________ Period _______ Justify by stating the key definition, postulate or theorem. 1. Find the value of AB if AC =19. Justify your work. 3a – 10 4a + 1 A B C ====================================================== 2. Find the value of x. Justify your work. (30x + 23)° (20x + 7)° ====================================================== INSURANCE QUESTION 3. Construct a square with side length ½ SQ. S Q ====================================================== 4. What theorem justifies the following statement? If ≮ 7 ≮ 8 are supplementary, and ≮ 7 ≮ 9 are supplementary, then ≮ 8 ≅ ≮ 9. ====================================================== 5. Line a is perpendicular to line c. Line b is also perpendicular to line c. How are lines a and b related? Draw the figure and justify. ====================================================== INSURANCE QUESTION 6. Find the measure of ≮ . Justify your work. L M 47° 43° A B N Answer Column. Show your work on a separate sheet of paper. Thank you. 1. 6 pts 2 AB=2; 2 – work shown; 2 justification 2. 6 pts 2 – x=3; 2 work shown; 2 justification 3. See Diagram 4 2 pts 5. 6 pts 2 – a is parallel to b 2 – drawing w/ label 2 justification 6.
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Midterm #1 -‐ -‐ Chapters 1-‐3 Name ____________________________ Geometry Date _____________ Period _______ Justify by stating the key definition, postulate or theorem. 1. Find the value of AB if AC =19. Justify your work.
3a – 10 4a + 1 A B C ====================================================== 2. Find the value of x. Justify your work. (30x + 23)° (20x + 7)° ====================================================== INSURANCE QUESTION 3. Construct a square with side length ½ SQ. S Q ====================================================== 4. What theorem justifies the following statement?
If ≮ 7 𝑎𝑛𝑑 ≮ 8 are supplementary, and ≮ 7 𝑎𝑛𝑑 ≮ 9 are supplementary, then ≮ 8 ≅ ≮ 9.
====================================================== 5. Line a is perpendicular to line c. Line b is also perpendicular to line c. How are lines a and b related? Draw the figure and justify. ======================================================
INSURANCE QUESTION 6. Find the measure of ≮ 𝑳𝑩𝑵. Justify your work.
L M 47° 43° A B N
Answer Column. Show your work on a separate sheet of
paper. Thank you. 1. 6 pts 2 -‐ AB=2; 2 – work shown; 2-‐ justification 2. 6 pts 2 – x=3; 2-‐ work shown; 2-‐ justification 3. See Diagram 4 2 pts 5. 6 pts 2 – a is parallel to b 2 – drawing w/ label 2 -‐ justification 6.
7. Reorder the reasons of the following proof to match the correct statements. 1 2 a 3 b Given: ≮ 𝟏 𝒊𝒔 𝒔𝒖𝒑𝒑𝒍𝒆𝒎𝒆𝒏𝒕𝒂𝒓𝒚 𝒕𝒐 ≮ 𝟑 Prove: 𝒂 𝒊𝒔 𝒑𝒂𝒓𝒂𝒍𝒍𝒆𝒍 𝒕𝒐 𝐛
Statements Reasons 1. ≮ 1 𝑖𝑠 𝑠𝑢𝑝𝑝𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦 𝑡𝑜 ≮ 3
a. Angles that form a straight angle are supplementary
2. ≮ 1 𝑖𝑠 𝑠𝑢𝑝𝑝𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦 𝑡𝑜 ≮ 2 b. Converse of the Corresponding Angles Theorem
3. ≮ 2 ≅≮ 3 c. Given 4. 𝑎 𝑖𝑠 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑡𝑜 b d. Congruent
Supplements Theorem
====================================================== 8. What is the intersection of planes ABFE and BCGF? D C A B H G E F ====================================================== 9. Find the area of a circle with circumference 𝟏𝟔𝝅 𝒎. ====================================================== 10. Given K(2, -‐4) and M(4,8), the midpoint of 𝐊𝐆, find the coordinates of G using the midpoint formula.
Answer Column. Show your work on a separate sheet of
paper. Thank you. 7. Place the number (#1-‐4) under the statements columns and letter (#a-‐d) under the reasons column. (see your diagram) Statements Reasons
1 pt
1 pt
1 pt
1 pt
8. 2 pts 9. 6 pts 2 -‐ 64𝝅; 2 – work shown; 2 – units 10. 6 pts. 2 – (6,20); 2 – formula work shown x; 2 – formula work shown y
11. Given the line y = -‐3x + 5,
a. Write the equation of the line that is perpendicular and contains (-‐3,4).
b. Write the equation of the line that is parallel and goes through the origin. ====================================================== 12. What conditions in the figure below will prove 𝒍 ∥ 𝒎 ? l 1 2 4 m 3 ====================================================== 13. Using the distance formula, find the length of 𝐀𝐁, 𝐠𝐢𝐯𝐞𝐧 𝑨 𝟗,−𝟖 𝒂𝒏𝒅 𝑩(𝟏,−𝟒). Leave answer in radical form. ====================================================== 14. Find the values of x, y and z. Justify your work. A B x° 35° z° 95° y° 35° C D ======================================================
Answer Column. Place only answers here. Show your work on a separate sheet of
paper. Thank you. 11. 4 pts a. 2 pts b. 2 pts 12. 6 pts 2 pts each of 3 correct responses (-‐2) pts for each invalid reason 13. 4 pts 2 – numerical answer (simplified) ; 2 – work with formula 14. 12 pts x = 2pts – 90 deg; 2 pts -‐ justification y = 2 pts – 60 deg; 2 pts -‐ justification z = 2 pts – 85 deg; 2 pts -‐ justification
15. In the proof below, identify the reason that is missing for the corresponding statement. 4 1 3 2 5 Given: m ≮ 4 = 𝑚 ≮ 5 = 135 Prove: ≮ 3 is a right angle.
6. 𝑚 ≮ 1+𝑚 ≮ 2+𝑚 ≮ 3 = 180 6. ? 7. 45+ 45+𝑚 ≮ 3 = 180 7. Substitution 8. 𝑚 ≮ 3 is 90 8. ? 9. ≮ 3 is a right angle. 9. ? ====================================================== Create a 2-‐column proof for problems #16 and #17.
16. Given: 𝒙 = 𝟐𝟎 Prove: 𝒂 ∥ 𝒃
60°
a b
3x°
====================================================== 17. Given: 𝑹𝑼 ∥ 𝑺𝑻 ; ≮ 𝑹 ≅ ≮ 𝑻 Prove: 𝑹𝑺 ∥ 𝑼𝑻 R 3 S
2 1 4 U T
Answer Column. Place only answers here. Show your work on a separate sheet of
paper. Thank you. 15. 10 pts Reasons 1. 2pts 3. 2pts 6. 2pts 8. 2 pts 9. 2pts 16. Use a separate sheet of paper to show your 2-‐column proof. 8pts 17. Use a separate sheet of paper to show your 2-‐column proof. 8pts