By Lorenza Luster and Helen Benyard Luster
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Extra info for Amsco's Virginia: Preparing for the SOL Geometry Test
A house lot is in the shape of the figure below. 120° C 110° 50° 130° x° 125° A F B Find the value of x. If the measure of ЄEDF is 50°, what is the measure of ЄADF? F 140° G 130° H 50° J 40° 5. 110° The pattern in Edward’s bathroom floor is made with tiles shaped like equilateral triangles. Find the value of x. A B C D 8. 70° 110° 125° 130° The banister of Carlton’s porch is shown below. x° 45° x A B C D 6. 30° 45° 60° 90° What is the measure of Є1 in the figure below? A B 100° 1 30° D F G H J 80° 50° 30° 20° 14 • Lines and Angles 100° 50° C Find the value of x in degrees.
Step 2. Q T T rise 6 Q Find the slope of AB. The slope of AB ϭ run ϭ . 5 Use point C to locate a new point D that has a rise of 6 units and a run of 5 units from point C. y run 5 run 5 D(11, 9) B(1, 7) rise 6 rise 6 C(6, 3) A(–4, 1) x A point that has a rise of 6 units and a run of 5 units from point C is D(11, 9). Therefore, the lines will be parallel if D is located at (11, 9). 18 • Lines and Angles 4 x + 48 2 x + 108 4 x + 48 2 x + 108 1. Which postulate or theorem justifies a ʈ b? a b 2. Which postulate or theorem justifies a ʈ b?
These are both true statements. Therefore, c ٙ d or “50 is an even number and 50 is a multiple of 5” is also a true statement. Translating A logical argument is a series of statements called premises or hypotheses folArguments Into lowed by a final statement called the conclusion. We say that the conclusion Symbolic Form logically follows the premises if, by the laws of reasoning, the premises force the conclusion to be true. An argument satisfying this condition is called a valid argument. We will review arguments that use the law of detachment (modus ponens), the law of the contrapositive (modus tollens), and the law of syllogism (the chain rule).