By Lorenza Luster and Helen Benyard Luster
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Additional info for Amsco's Virginia: Preparing for the SOL Geometry Test
Given: CD. C D Construct a line segment AX congruent to line segment CD. 22 • Lines and Angles Straightedge and Compass: Step 1. Use your straightedge to draw a line on your paper. Choose any point on that line and label it point A. Step 2. Adjust your compass to correspond to the length of CD. Step 3. A Without changing the compass setting, place the tip of your compass on point A and draw an arc that intersects the line. Label the intersection X. C D A X Result: Since we adjusted our compass to the length of CD, AX Х CD.
Rewrite the hidden conditional. Conditional: If a quadrilateral is a rectangle, then it is a parallelogram. Contrapositive: If a quadrilateral is not a parallelogram, then it is not a rectangle. ” Thus, a conditional and its contrapositive always have the same truth values. However, the same is not true of converses and inverses: a conditional can be true, but its converse and inverse can both be false. Model Problem 5 Solution Given the statement, “If two angles are right angles, then they are congruent,” write its converse and determine the truth value of the converse.
With A as the center, draw an arc below line t. A B X Step 3. With the same compass setting, place the tip of the compass on B and draw an arc below line t. Label the intersection Y. B t A Y Constructions with Compass and Straightedge—Working with Angles • 25 Step 4. X Use your straightedge to draw a line through X and Y. A B Y Q T Result: XY is perpendicular to line t and passes through the point X. Note: If X is below the line segment, simply turn the figure over and follow the same instructions as before, starting from Step 1.
Amsco's Virginia: Preparing for the SOL Geometry Test by Lorenza Luster and Helen Benyard Luster