Explain it

01.10 — 4 short write-ups

Question 1 of 4

A checkpoint, not a test

Part One Reasoning Check — Question 1 of 4

Optional explanation practice using only Module 01 material. This does not submit the Canvas exam.

An original angle at A and a new ray from D with matching construction arcs
The original angle is at A, and the new ray begins at D. Matching arcs have already been drawn from A and D. Explain the remaining compass-and-straightedge steps needed to finish the congruent angle at D. Include which distance must be copied and why the compass width must stay fixed.

Look at the two places where the first arc crosses the original angle. What distance between those points controls the angle opening?

Question 2 of 4

A checkpoint, not a test

Part One Reasoning Check — Question 2 of 4

Angle relationship and algebra. Show each important reason.

Two parallel horizontal lines cut by a slanted transversal, with angles 1 through 8 labeled
The two horizontal lines are parallel. Angles 4 and 5 measure (6x + 12)° and (4x + 18)°. Identify their relationship, write the equation, solve for x, and find both angle measures. Name the reason for the 180° equation and the main algebra steps.

Angles 4 and 5 are between the parallel lines and on the same side of the transversal.

Question 3 of 4

A checkpoint, not a test

Part One Reasoning Check — Question 3 of 4

Theorem proof. Prove the result instead of naming the result as your reason.

Two lines intersecting at E, forming angles 1 through 4
Use the diagram to prove that angle 1 is congruent to angle 3 without using the Vertical Angles Theorem as a reason. Start with two straight-angle sums, show why those sums are equal, subtract the shared neighboring angle, and finish with the definition of congruent angles.

Angles 1 and 2 form one straight angle. Angles 2 and 3 form another.

Question 4 of 4

A checkpoint, not a test

Part One Reasoning Check — Question 4 of 4

Proof chain. Use known theorems to reach the requested angle pair.

Two parallel horizontal lines cut by a slanted transversal, with angles 1 through 8 labeled
The two horizontal lines are parallel. Prove that angle 2 is congruent to angle 8 using the Corresponding Angles Theorem, the Vertical Angles Theorem, and the Transitive Property. State each congruent pair in order. Do not use the Alternate Exterior Angles Theorem as a reason because that is the result you are proving.

First connect angle 2 to angle 6. Then connect angle 6 to angle 8.