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