A proof states that two lines intersect, and concludes that the angles opposite each other at the intersection are congruent. Which result justifies that conclusion?

In a proof, a step is written whose justification is that two sides of a triangle are congruent. Which result is being used?

A proof states that one side of a triangle is extended past a vertex, and concludes that the exterior angle equals the sum of the two remote interior angles. Which result justifies that conclusion?

In circle O, an inscribed angle measures 6x + 4 degrees and it intercepts an arc measuring 4x + 72 degrees. Which equation follows from the Inscribed Angle Theorem?

A proof states that two angles of one triangle are congruent to two angles of another, and concludes that the triangles are similar. Which result justifies that conclusion?

Lines m and n are parallel, and a transversal forms alternate interior angles measuring 6x + 4 degrees and 2x + 36 degrees. Which equation follows from the Alternate Interior Angles Theorem?

Two angles of one triangle are congruent to two angles of another triangle. Which conclusion does this justify?

A proof states that all three pairs of corresponding sides of two triangles are proportional, and concludes that the triangles are similar. Which result justifies that conclusion?

In a proof, a step is written whose justification is that two angles and the INCLUDED side of one triangle are congruent to those of another. Which result is being used?

Given that point P lies on the bisector of an angle, what does the Angle Bisector Theorem conclude?

Two RIGHT triangles have congruent hypotenuses and one congruent pair of legs. Which conclusion does this justify?

A proof states that line t is tangent to circle O at point P, and concludes that line t is perpendicular to radius OP. Which result justifies that conclusion?

A proof states that three lengths are given, and concludes that they form a triangle only if the two shortest add to more than the longest. Which result justifies that conclusion?

A proof states that a ray lies inside an angle, and concludes that the two smaller angles add to the whole angle. Which result justifies that conclusion?

In circle O, an inscribed angle measures 4x + 12 degrees and it intercepts an arc measuring 6x + 36 degrees. Which equation follows from the Inscribed Angle Theorem?

In a proof, a step is written whose justification is that a quadrilateral has all four vertices on a circle. Which result is being used?

Given that a triangle has a right angle, what does the Pythagorean Theorem conclude?

Given that point B lies between A and C, what does the Segment Addition Postulate conclude?

A proof states that two parallel lines are cut by a transversal, and concludes that alternate interior angles are congruent. Which result justifies that conclusion?

In circle O, an inscribed angle measures 7x + 8 degrees and it intercepts an arc measuring 6x + 64 degrees. Which equation follows from the Inscribed Angle Theorem?

A proof states that point P lies on the perpendicular bisector of segment AB, and concludes that PA = PB. Which result justifies that conclusion?

A proof shows that two sides of one triangle are proportional to two sides of another and the included angles are congruent, and concludes that the triangles are similar. Which result justifies that conclusion?

A proof states that two parallel lines are cut by a transversal, and concludes that same-side interior angles are supplementary. Which result justifies that conclusion?

Lines m and n are parallel, and a transversal forms same-side interior angles measuring 6x + 4 degrees and 2x + 36 degrees. Which equation follows from the Same-Side Interior Angles Theorem?

In a proof, a step is written whose justification is that two RIGHT triangles have congruent hypotenuses and one congruent pair of legs. Which result is being used?

Lines m and n are parallel, and a transversal forms alternate interior angles measuring 3x + 10 degrees and 2x + 20 degrees. Which equation follows from the Alternate Interior Angles Theorem?

In a proof, a step is written whose justification is that a segment joins two sides of a triangle and is parallel to the third side. Which result is being used?

A proof states that an angle bisector of a triangle meets the opposite side, and concludes that it divides that side in the ratio of the two adjacent sides. Which result justifies that conclusion?

Given that one side of a triangle is extended past a vertex, what does the Exterior Angle Theorem conclude?

In circle O, an inscribed angle measures 2x + 25 degrees and it intercepts an arc measuring 12x + 30 degrees. Which equation follows from the Inscribed Angle Theorem?

A proof states that ABC is any triangle, and concludes that the three interior angles total 180 degrees. Which result justifies that conclusion?

In a proof, a step is written whose justification is that point B lies between A and C. Which result is being used?

Given that a quadrilateral has all four vertices on a circle, what does the Inscribed Quadrilateral Theorem conclude?

Given that D and E are the midpoints of two sides of triangle ABC, what does the Triangle Midsegment Theorem conclude?

Given that three lengths are given, what does the Triangle Inequality Theorem conclude?

Given that point P lies on the perpendicular bisector of segment AB, what does the Perpendicular Bisector Theorem conclude?

In a proof, a step is written whose justification is that an angle has its vertex on a circle and stands on an arc. Which result is being used?

Two angles and the INCLUDED side of one triangle are congruent to those of another triangle. Which conclusion does this justify?

Given that two sides of a triangle are congruent, what does the Base Angles Theorem conclude?

Lines m and n are parallel, and a transversal forms alternate interior angles measuring 3x + 22 degrees and 5x + 8 degrees. Which equation follows from the Alternate Interior Angles Theorem?