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Geometry Chapter 7 Post-Test Worksheet KEY Problem # Concept Properties of Quadrilaterals: Verify, apply and prove properties of quadrilaterals. 1-4 Mastered Needs Retake 1. Prove the following using either a two column proof or a flow chart. Make sure to include all of your reasons to support your statements. H M Given: K is the midpoint of ฬ ฬ ฬ ฬ ๐ฝ๐ and๏๐ป๐ฝ๐พ ๏ ๏๐ฟ๐๐พ Prove: ฬ ฬ ฬ ฬ โ ๐ฟ๐ ฬ ฬ ฬ ฬ ๐ป๐ฝ J K L STATEMENT 1) K is the midpoint of ฬ ฬ ฬ ฬ ๐ฑ๐ด 2) JK = MK 3) โ ๐ฏ๐ฑ๐ฒ โ ๐ณ๐ด๐ฒ โ 4) โ ๐ฏ๐ฒ๐ฑ โ โ ๐ณ๐ฒ๐ด 5) โ๐ฏ๐ฒ๐ฑ โ โ๐ณ๐ฒ๐ด ฬ ฬ ฬ ฬ โ ฬ ฬ ฬ ฬ ฬ 6) ๐ฏ๐ฑ ๐ณ๐ด JUSTIFICATION 1) Given 2) Definition of midpoint 3) Given 4) Vertical Angles are โ 5) ASA โ 6) โ โ๐ฌ โถโ ๐ฉ๐๐ซ๐ญ๐ฌ 2. Prove that if a pair of opposite sides of a quadrilateral is congruent and parallel, then the quadrilateral must ฬ ฬ ฬ ฬ โฅ ๐ถ๐ท ฬ ฬ ฬ ฬ and ๐ด๐ต ฬ ฬ ฬ ฬ โ ๐ถ๐ท ฬ ฬ ฬ ฬ , prove be a parallelogram. For example, for the quadrilateral ABCD shown, given that ๐ด๐ต ฬ ฬ ฬ ฬ ฬ ฬ ฬ ฬ that ๐ต๐ถ โฅ ๐ด๐ท . Organize your reasoning in the two column proof. B A 1. ฬ ฬ ฬ ฬ ๐จ๐ฉ โฅ ฬ ฬ ฬ ฬ ๐ซ๐ช 1. Given 2. โ ๐จ๐ช๐ซ โ โ ๐ช๐จ๐ฉ 2. Alternate Interior Angles ฬ ฬ ฬ ฬ ๏ ๐ถ๐ท ฬ ฬ ฬ ฬ 3. ๐ด๐ต 3. Given 4. ฬ ฬ ฬ ฬ ๐จ๐ช โ ฬ ฬ ฬ ฬ ๐จ๐ช 4. Reflexive Property 5. โABC ๏ โCDA 5. SAS โ 6. โ ๐จ๐ช๐ฉ โ โ ๐ช๐จ๐ซ 6. โ โs โถโ parts ฬ ฬ ฬ ฬ โฅ ฬ ฬ ฬ ฬ 7. ๐ต๐ถ ๐ด๐ท 7. AIA โ โถโฅ ๐๐ข๐ง๐๐ฌ C D Geometry Chapter 7 Post-Test Worksheet KEY 3. Fill-in the blank with the Definition of each Quadrilateral. (Hint: use your glossary.) A) Rhombus: quadrilateral with 4 congruent sides. B) Square: quadrilateral with 4 right angles and 4 congruent sides. C) Parallelogram: quadrilateral with 2 pairs of parallel sides. D) Kite: quadrilateral with 2 distinct pairs of consecutive congruent sides. E) Trapezoid: quadrilateral with at least one pair of parallel sides. S 4. In the figure at right, SL = 48cm and SI= 16cm. a. State why ๏SMI ~ ๏SLE . Be specific and make your explanation complete. M I L E [Angle S is congruent to itself by the identity property. The ratios of sides SM/SL and SI/SE are both ½. Therefore by SAS ~, โSMI ~ โSLE.] b. Find all side lengths of ๏SMI and ๏SLE . SHOW ALL WORK. SM = 24cm, SE = 32cm, MI โ 28.84cm, LE โ 57.69cm c. Is MI // LE ? Justify your conclusion. [Yes. โ ๐บ๐ด๐ฐ โ โ ๐บ๐ณ๐ฌ (๐ฌ๐ข๐ฆ๐ข๐ฅ๐๐ซ ๐ญ๐ซ๐ข๐๐ง๐ ๐ฅ๐๐ฌ ๐ก๐๐ฏ๐ โ ๐๐ง๐ ๐ฅ๐๐ฌ), ๐๐ ฬ ฬ ฬ ฬ ๐ด๐ฐ โฅ ฬ ฬ ฬ ฬ ๐ณ๐ฌ ๐๐๐๐๐ฎ๐ฌ๐ if corresponding angles are congruent, then lines are parallel.] Geometry Chapter 7 Post-Test Worksheet KEY Problem # Concept Midpoint, Distance and Slope: Use midpoint, distance and slope properties to determine relationships between line 1-4 segments. Mastered Needs Retake 1. For the segment with endpoints A(1, 6) and B(3, 8) a. Find the midpoint of line segment ฬ ฬ ฬ ฬ ๐ด๐ต . [(2, 7)] ฬ ฬ ฬ ฬ . b. Find the length of line segment ๐ด๐ต [โ 2.83 units] ฬ ฬ ฬ ฬ name the coordinates of point C. c. If point A is the midpoint of ๐ต๐ถ [C(-1, 4)] 2. Plot the points A (0, 0), B (8,0), C (8,6), D (2,6). What shape is ABCD (name it completely)? Use the length & slope of each side to justify your conclusion. Show All Work ฬ ฬ ฬ ฬ ๐๐ ๐๐๐๐ & ๐ ๐๐๐๐ ๐๐ ๐ฉ๐ช ฬ ฬ ฬ ฬ ๐๐ ๐๐๐ ๐๐๐๐๐๐ , ๐๐ ๐ฉ๐ช ฬ ฬ ฬ ฬ โฅ ฬ ฬ ฬ ฬ ๐๐๐ ๐ช๐ซ [๐๐๐๐๐ ๐๐ ๐จ๐ฉ ฬ ฬ ฬ ฬ ฬ ฬ ฬ ฬ ฬ ฬ ฬ ฬ ๐จ๐ฉ ๐๐๐ ๐ช๐ซ. ๐ป๐๐ ๐๐๐๐๐ ๐๐ ๐ซ๐จ ๐๐ ๐, so its angles are not 90°. ABCD is a right trapezoid b/c it has 2 right angles and 1 pair of parallel sides.] Geometry Chapter 7 Post-Test Worksheet KEY 3. Find the midpoint of segment ฬ ฬ ฬ ฬ ๐ด๐ต , if A(-4, 9) and B(-13, -18) [(-8.5, -4.5)] 4. Plot and connect the points S (0, 0) T (0, 5), A (4, 6), R (7, 2) to form quadrilateral STAR. What shape is STAR? Use the slope of the sides to justify your answer completely. [quadrilateral: no slopes are congruent or opp. inverse, so no parallel or perpendicular sides.]