1 / 5

Understanding Angles Through Corresponding and Vertical Angles Theorems

This text explains the identification and calculation of angles using the Corresponding Angles Postulate and the Vertical Angles Congruence Theorem. It describes how angles can be measured and related through properties of parallel lines. The document includes examples showing how to find unknown angles, along with the necessary steps and reasoning. Key concepts like vertical angles, corresponding angles, and supplementary angles are illustrated, providing a comprehensive understanding of angle relationships in geometry.

flint
Télécharger la présentation

Understanding Angles Through Corresponding and Vertical Angles Theorems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The measure of three of the numbered angles is 120°. Identify the angles. Explain your reasoning. By the Corresponding Angles Postulate, m5=120°. Using the Vertical Angles Congruence Theorem, m4=120°. Because 4 and 8 are corresponding angles, by the Corresponding Angles Postulate, you know that m8 = 120°. EXAMPLE 1 Identify congruent angles SOLUTION

  2. ALGEBRA Find the value of x. By the Vertical Angles Congruence Theorem, m4=115°. Lines aand bare parallel, so you can use the theorems about parallel lines. m4 + (x+5)° 180° = 115° + (x+5)° 180° = Substitute 115° for m4. x + 120 = 180 x = 60 EXAMPLE 2 Use properties of parallel lines SOLUTION Consecutive Interior Angles Theorem Combine like terms. Subtract 120 from each side.

  3. Use the diagram at the right. 1. If m 1 = 105°, find m 4, m 5, and m 8. Tell which postulate or theorem you use in each case. m 4 = m 5 = m 8 = 105° 105° 105° for Examples 1 and 2 GUIDED PRACTICE SOLUTION Vertical Angles Congruence Theorem. Corresponding Angles Postulate. Alternate Exterior Angles Theorem

  4. Use the diagram at the right. 2. If m 3 = 68° and m 8 = (2x + 4)°, what is the value of x? Show your steps. for Examples 1 and 2 GUIDED PRACTICE

  5. 180° m 7 + m 8 = m 7 m 3 = 68° 68° + 2x + 4 = 180° Substitute 68° for m 7 and (2x + 4)for 8. 7 and 5 are supplementary. 72 + 2x = 180° m 3 = 2x = 108 x = 54 for Examples 1 and 2 GUIDED PRACTICE SOLUTION Corresponding Angles Postulate. Combine like terms. Subtract 72 from each side. Divide each side by 2.

More Related