Directions: Examine each proof and determine the missing entries. After clicking the drop-down box, if you arrow down to the answer, it will remain visible. There may be more than one way to solve these problems. These solutions show one possible solution.

 1
 Statements Reasons 1. 1. Reason Given 2. 2. Reason Midpoint of a segment divides the segment into two congruent segments. 3. 3. Reason ASA - If 2 angles and the included side of one triangle are congruent to the corres. parts of another triangle, the triangles are congruent.

 2
 Statements Reasons 1. 1. Reason Given 2. 2. Reason Segment bisector forms two congruent segments. 3. 3. Reason Vertical angles are congruent. 4. 4. Reason SAS - If 2 sides and the included angle of one triangle are congruent to the corres. parts of another triangle, the triangles are congruent.

 3
 Statements Reasons 1. 1. Reason Given 2. 2. Reason An angle bisector is a ray in the in the interior of an angle that forms two congruent angles. 3. ∠ADB, ∠ADC right angles 3. Reason Perpendicular lines meet to form right angles. 4. 4. Reason All right angles are congruent. 5. 5. Reason Reflexive property (shared side) 6. 6. Reason ASA - If 2 angles and the included side of one triangle are congruent to the corres. parts of another triangle, the triangles are congruent.

 4
 Statements Reasons 1. 1. Reason Given 2. ∠ABC, ∠ADC right angles 2. Reason Perpendicular lines form right angles. 3. ΔABC,  ΔADC right triangles 3. Reason A right triangle contains a right angle. 4. 4. Reason Reflexive property (shared side). 5. 5. Reason HL - If the hypotenuse and leg of one right triangle are congruent to the corres. parts of another right triangle, the right triangles are congruent.

 5
 Statements Reasons 1. 1. Reason Given 2. 2. Reason Isosceles triangles have 2 congruent sides. 3. 3. Reason If 2 sides of a triangle are congruent, the angles opposite them are congruent. 4. 4. Reason Altitude of a triangle is a segment from any vertex perpendicular to the line containing the opposite side. 5. ∠BDA, ∠BDC right angles 5. Reason Perpendicular lines form right angles. 6. 6. Reason All right angles are congruent. 7. 7. Reason AAS - If two angles and the non-included side of one triangle are congruent to the corres. parts of another triangle, the triangles are congruent.