Geometry // Writing a Two-Column Proof

linear pair

A pair of adjacent angles whose noncommon sides are opposite rays.

vertical angles

A pair of opposite congruent angles formed by intersecting lines

Complete the paragraph proof to prove the statement. Given: ∠ABC ≅ ∠DEF and ∠GHI ≅ ∠DEF Prove: m∠ABC = m∠GHI We are given that angle ABC and _ are congruent, and that angle GHI and angle DEF are congruent. By the _ , the measure of angle ABC is equal to the measure of angle DEF, and the measure of angle GHI is equal to the measure of angle DEF. By the substitution property, the measure of angle ABC is equal to _.

1) angle DEF 2) definition of congruent angles 3) the measure of angle GHI

Which statements are correct? Check all that apply.

A compass is used to make circles and arcs in geometric constructions. Geometric constructions are created with a compass and straightedge.

perpendicular bisector

A line that is perpendicular to a segment at its midpoint.

Given: angle ABC congruent to angle DEF and GHI congruent to DEF Prove: length ABC = length GHI

ABC congruent to DEF reason given GHI congruent to DEF reason given DEF congruent to GHI reason symmetric property ABC congruent to GHI reason transitive property length ABC = length GHI reason definition of congruent angles

adjacent angles

Angles that have a common side and a common vertex (corner point).

supplementary angles

Two angles whose sum is 180 degrees

complementary angles

Two angles whose sum is 90 degrees

Straightedge

a ruler with no markings on it

With diagrams, you can allowed to assume

adjacent angles, vertical angles, linear pairs, collinear points, opposite rays

congruent angles

angles that have the same measure

flow chart proof

given, sym prop, trans prop, def of line seg

compass

navigational instrument for finding directions

First proof is the symmetric property, where if AB = CD then CD must be = AB. Second we have the Reflexive property, which basically means a segment like CD is congruent to EF. Last but not least Transitive property, meaning MN = XY and XY = AB then MN = AB.

properties

With diagrams you are not allowed to assume

segment measure, angle measure, parallel lines, perpendicular lines