Line and angle proofs

Line and angle proofs
Description
Exercise Name:	Line and angle proofs
Math Missions:	High school geometry Math Mission
Types of Problems:	2

The Line and angle proofs exercise appears under the High school geometry Math Mission. This exercise uses lines and angles to establish facts via rigorous proof.

Types of Problems

There are two types of problems in this exercise:

1. Fill in the spaces to complete the proof: This problem has a proof of a statement with missing spaces. The student is asked to use the included diagram to fill in the template with statements that will complete the proof correctly.

   

   Fill in the spaces to complete the proof

2. Select the best reasoning: This problem makes a true claim. The student is asked to select which line of reasoning best establishes the fact that is being claimed from a multiple choice list.

   

   Select the best reasoning

Strategies

Knowledge of line and angle theorems being proved would assist with accuracy and efficiency, but generally only basic definitions are needed to ensure success on this exercise.

1. Complementary angles add up to ${90^\circ}$ and supplementary angles add up to ${180^\circ}$.
2. The last line of a proof is generally the statement that was supposed to be proved.
3. A complement to an angle that measures ${x^\circ}$ is ${90-x^\circ}$, and a supplement is ${180^\circ}$.
4. Some of the proofs call upon the triangle congruence theorems (for example, SAS or SSS).

Real-life Applications

1. Understanding the relationships between angles is important in drafting, mapping and architecture.
2. Engineers and architects use angles for designs, roads, buildings and sporting facilities.
3. Athletes use angles to enhance their performance. Carpenters use angles to make chairs, tables and sofas.
4. Artists use their knowledge of angles to sketch portraits and paintings.