2.11 Practice Test: Reasoning and Proof

A conjecture and the two column proof are used to prove the conjecture are shown given angle one is supplementary to angle two BD bisects angle ABC prove angle one is supplementary to angle three

2. angle one and angle two equals 180° 4.definition of a bisector 5. M1 plus M3 equals 180° 5. substitution property of equality

A conjecture, and the two column proof used to prove the conjecture are shown given angle one equals 90° prove triangle PQR is a right triangle

2. angle one is congruent to angle 2 3. Angle congruence 4. Angle two equals 90°. 6. Definition of a right triangle.

A conjecture and the paragraph proof used to prove the conjecture are shown. Given: <2 = <3 Prove: <1 and <3 are supplementary.

<1 and <2 form a linear pair, so <1 and <2 are supplementary by the linear pair postulate. Therefore, m<1+m<2=180* by the definition of supplementary. It is given that <2 is congruent to <3, so M<2 equals M<3 by the angle congruence postulate. By substitution M<1+M<3 equals 180°, so angle one and angle 3 are supplementary by the definition of supplementary.

A conjecture in the flowchart proof used to prove the conjecture are shown. angle three is congruent to angle two prove line sector, DC bisects angle ADE

ABCD is a parallelogram given line sector 80 is parallel to line sector. DC definition of a parallelogram angle one is congruent to angle three corresponding angles. Postulate angle three is congruent to angle to given angle. One is congruent to angle to transitive property of... line sector, DC bisects angle ADE, definition of a bisector

Chloe draws three parallelograms. In each figure, she measures a pair of angles, as shown. What is a reasonable conjecture for Chloe to make by recognizing a pattern and using inductive reasoning?

In a parallelogram, consecutive angles are supplementary.

Jasmine draws three scalene triangles. In each figure, she measures each of the angles In a scalene triangle, one of the angles is obtuse

In a scalene triangle, none of the angles are congruent.

Which statement is true about this argument? Premises: If a triangle has an angle that measures 150°, then it is an obtuse triangle. <JKL is an obtuse triangle. Conclusion <JKL has an angle that measures 150°

The argument is not valid because the conclusion does not follow from the premises.

Which statement is true about this argument? Premises: If two lines are parallel, then the lines do not intersect Lines m and n do not intersect. Conclusion: Lines m and n are parallel. Which statement is true about the argument?

The argument is not valid because the conclusion does not follow from the premises.

Which statement is true about this argument? Premises: If a quadrilateral is a square, then the quadrilateral is a rectangle. If a quadrilateral is a rectangle, then the quadrilateral is a parallelogram.

The argument is valid by the law of syllogism.

Jamar draws three pairs of parallel lines that are each intersected by a third line. In each figure, he measures a pair of same-side interior angles. What is a reasonable conjecture for Jamar to make by recognizing a pattern and using inductive reasoning?

When a pair of parallel lines are intersected by a third line, the same-side interior angles are supplementary.

A conjecture and the flowchart proof used to prove the conjecture are shown. Given: m<DEG = 51° m<GEF = 39° Prove: 🔼DEF is a right triangle.

given. Angle addition postulate. 51° +39° equals Angle DEF. 90° equals M <DEF. <DEF is a right angle.definition of right triangle.

given: JKLM is a parallelogram <2 is congruent to <3 prove: <1 is congruent to <3

it is given that JKLM as a parallelogram, so line segment JM is parallel to line segment KL by the definition of parallelogram. Therefore, angle one is congruent to angle two by the corresponding angles postulate. Also, it is given that angle two is congruent to angle three so angle one is congruent to angle three by the transitive property of congruence