๐ Topic Summary
Geometric proofs involving angle relationships use theorems and postulates to logically demonstrate the truth of statements about angles. These proofs often rely on angle properties like complementary angles (adding up to $90^{\circ}$), supplementary angles (adding up to $180^{\circ}$), vertical angles (equal when formed by intersecting lines), and the angle addition postulate. Mastering these relationships is crucial for solving geometric problems and building a solid foundation in geometry.
The key to success is understanding the definitions and properties of different angle pairs and how they relate to each other. Using deductive reasoning, you can start with given information and build a chain of logical steps to arrive at the desired conclusion. Now, let's put that knowledge to the test with some practice!
๐ Part A: Vocabulary
Instructions: Match each term with its correct definition.
| Term |
Definition |
| 1. Complementary Angles |
A. Two angles that share a common vertex and side, but do not overlap. |
| 2. Supplementary Angles |
B. An angle whose measure is exactly $90^{\circ}$. |
| 3. Vertical Angles |
C. Two angles whose measures add up to $90^{\circ}$. |
| 4. Adjacent Angles |
D. Two non-adjacent angles formed by intersecting lines; they are congruent. |
| 5. Right Angle |
E. Two angles whose measures add up to $180^{\circ}$. |
โ๏ธ Part B: Fill in the Blanks
Instructions: Fill in the blanks with the correct terms.
If two lines intersect, then the __________ angles formed are congruent. Two angles are considered __________ if they share a common vertex and side but do not overlap. If the non-common sides of two adjacent angles form a straight line, then these angles are __________. Angles that add up to $90^{\circ}$ are called __________ angles, while angles that add up to $180^{\circ}$ are called __________ angles.
๐ค Part C: Critical Thinking
Instructions: Answer the following question with a detailed explanation.
Explain how you can use the properties of vertical angles and supplementary angles to find the measure of all four angles formed by two intersecting lines, if you only know the measure of one of the angles.