grover
Uploaded by
13 SLIDES
228 VUES
130LIKES

Proportional Parts in Triangles

DESCRIPTION

Explore how to identify and calculate proportional parts in triangles using midsegments and parallel lines. Learn key theorems and concepts to solve problems effectively.

1 / 13

Télécharger la présentation

Proportional Parts in Triangles

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. Ch 9.5 DG = FH DE ? D Complete the proportion. x FE G Suppose DE=15, find x. 3   Suppose DE=15, find EG. 12 F E 2 8 H Find the value of y. 12 14 18   y + 3 y

  2. Ch 9.5 Learning Target: I will be able to use proportions to determine whether lines are parallel to sides of triangles. Standard 7.0 Students use theorems involving the properties of parallel lines cut by a transversal. Ch 9.5Proportional Parts

  3. Ch 9.5 midsegment of a triangle A segment of a triangle is called a midsegment when its endpoints are the midpoints of two sides of the triangle. A Midpoint of AC Midpoint of AB B C Vocabulary

  4. Ch 9.5 Theorem 9-6 Concept

  5. Ch 9.5 Since the sides are proportional. In order to show that we must show that Answer: Since the segments have proportional lengths, GH || FE. Determine if Lines are Parallel Example 2

  6. Ch 9.5 A. yes B. no C. cannot be determined Example 2

  7. Ch 9.5 Theorem 9-7 Concept

  8. Ch 9.5 ED = AB Triangle Midsegment Theorem A. In the figure, DE and EF are midsegments of ΔABC. Find AB. 5 = AB Substitution 1 1 __ __ 2 2 Use the Triangle Midsegment Theorem 10 = AB Multiply each side by 2. Answer:AB = 10 Example 3

  9. Ch 9.5 FE = BC Triangle Midsegment Theorem B. In the figure, DE and EF are midsegments of ΔABC. Find FE. FE = (18) Substitution 1 1 __ __ 2 2 Use the Triangle Midsegment Theorem FE = 9 Simplify. Answer:FE = 9 Example 3

  10. Ch 9.5 C. In the figure, DE and EF are midsegments of ΔABC. Find mAFE. By the Triangle Midsegment Theorem, AB || ED. Use the Triangle Midsegment Theorem AFEFED Alternate Interior Angles Theorem mAFE = mFED Definition of congruence mAFE = 87 Substitution Answer:mAFE= 87 Example 3

  11. Ch 9.5 A. In the figure, DE and DF are midsegments of ΔABC. Find BC. A. 8 B. 15 C. 16 D. 30 Example 3

  12. Ch 9.5 B. In the figure, DE and DF are midsegments of ΔABC. Find DE. A. 7.5 B. 8 C. 15 D. 16 Example 3

  13. Ch 9.5 C. In the figure, DE and DF are midsegments of ΔABC. Find mAFD. A. 48 B. 58 C. 110 D. 122 Example 3

More Related