Directions: Using the GIVEN information, draw a conclusion and support it with a REASON (definition, theorem or postulate). It may be the case that more than one conclusion is possible (but only one possible solution will be stated here).

 1 Given: ∠B is a right angle Conclusion: Conclusion: m∠B = 90º. Reason: Reason: A right angle has a measure of 90º.

 2 Given: intersect at E. Conclusion: Conclusion: ∠CEA ≅ ∠DEB or ∠CEB ≅ ∠DEA Reason: Reason: Vertical angles are congruent.

 3 Given: Conclusion: Conclusion: M is the midpoint of segment BC. Reason: Reason: A median of a triangle is a segment from any vertex to the midpoint of the opposite side.

 4 Given: ∠1 and ∠2 are complementary Conclusion: Conclusion: m∠1 + m∠2 = 90º. Reason: Reason: Complementary angles are 2 angles the sum of whose measures is 90º.

 5 Given: Conclusion: Conclusion: segment CD ⊥ segment AB Reason: Reason: An altitude of a triangle is a segment from any vertex perpendicular to the line containing the opposite side.

 6 Given: Conclusion: Conclusion: AB = CD Reason: Reason: Congruent segments have equal lengths.

 7 Given: ΔADB is isosceles, base Conclusion: Conclusion: segment AD ≅ segment AB Reason: Reason: An isosceles triangle has 2 congruent sides.

 8 Given: ∠1 ∠2 Conclusion: Conclusion: Ray BD bisects ∠ABC. Reason: Reason: An angle bisector is a ray from the vertex, and in the interior, of the angle forming two congruent angles.

 9 Given: mid-segment Conclusion: Conclusion: Segment MN || segment AB; MN = ½ AB Reason: Reason: Mid-segment of a triangle (connecting midpoint of one side to midpoint of another side) is parallel to the third side and half of its length.

 10 Given: ΔSTP Conclusion: Conclusion: m∠1 + m∠2 + m∠3 = 180º Reason: Reason: The sum of the measures of the angles in a triangle = 180º.