A conjecture and the two-column proof used to prove the conjecture are shown. Given: the measure of angle C B D equals 90 degrees. Prove: triangle A B C is a right triangle. Ray B D extends down and perpendicular from point B on segment B C. Drag an expression or phrase to each box to complete the proof. Statement Reason 1. m∠CBD=90° Given 2. ∠ABC and ∠CBD are supplementary. Response area 3. Response area Definition of supplementary 4. m∠ABC+90°=180° Response area 5. Response area Subtraction Property of Equality 6. ∠ABC is a right angle. Definition of right angle 7. △ABC is a right triangle. Definition of right triangle The option "Linear Pair Postulate" (3 of 4) has been grabbed. Press tab to choose where to drop it. Drop it by pressing the spacebar key. Cancel the operation by pressing escape.

Simplify. (-2)^-3 a. -8 b. -1/8 c. 1/8 d. 8

If a and −a are numbers on the number line, which expression must give the distance between them? a) 0 b) a c) |2a| d) |a|

Consider the following geometry problems in 3-space enter t or f depending on whether the statement is true or false. (you must enter t or f -- true and false will not work.) f equation editorequation editor 1. a plane and a line either intersect or are parallel t equation editorequation editor 2. two planes parallel to a third plane are parallel f equation editorequation editor 3. two lines either intersect or are parallel f equation editorequation editor 4. two planes orthogonal to a third plane are parallel f equation editorequation editor 5. two planes orthogonal to a line are parallel f equation editorequation editor 6. two planes either intersect or are parallel f equation editorequation editor 7. two lines orthogonal to a third line are parallel t equation editorequation editor 8. two lines parallel to a third line are parallel t equation editorequation editor 9. two planes parallel to a line are parallel f equation editorequation editor 10. two lines parallel to a plane are parallel f equation editorequation editor 11. two lines orthogonal to a plane are parallel