• Share
  • Email
  • Embed
  • Like
  • Save
  • Private Content
8 3 Similar Triangles
 

8 3 Similar Triangles

on

  • 3,792 views

 

Statistics

Views

Total Views
3,792
Views on SlideShare
3,783
Embed Views
9

Actions

Likes
0
Downloads
27
Comments
0

1 Embed 9

http://www.slideshare.net 9

Accessibility

Upload Details

Uploaded via as Microsoft PowerPoint

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

    8 3 Similar Triangles 8 3 Similar Triangles Presentation Transcript

    • Similar Triangles Focus – Apply the properties of similar triangles and tomorrow, prove that triangles are similar. Lesson 8-3 WA State Standards: G.3.A and G.3.B
    • Congruent Triangles …have matching angles that are congruent. …have matching sides that are congruent. A B C D F E 100° 35° 45° 115 ft 150 ft 100 ft 150 ft 115 ft 100 ft 35° 100° 45°
    • Congruent Triangles …have matching angles that are congruent. …have matching sides that are congruent. A B C D F E 100° 35° 45° 115 ft 150 ft 100 ft 150 ft 115 ft 100 ft 35° 100° 45°
    • Similar Triangles
      • IF and ONLY IF
        • Vertices match up so corresponding angles are congruent.
        • Corresponding sides are in proportion .
      30° 30° 75° 75° 75° 75° 16 12 12 16 6 8 Ratios of each side are
    • Triangle Similarity Postulate
      • If two angles of one triangle are equal in measure to two angles of another triangle,
      • then the two triangles are similar .
      • AA (angle/angle) similarity
    • AA?
      • You will also see:
      • SAS
      • ASA
      • SSS
      • Knowing these letters will help with proofs later .
      • Side/Angle/Side
      • Angle/Side/Angle
      • Side/Side/Side
    • Are they similar?
      • Only one angle is given as congruent. Two must be given to use Angle/Angle or AA Similarity .
    • Are they similar? Use Angle/Angle or AA Similarity . Two congruent angles show triangles are similar.
    • Similar?
      • Find the missing side of each triangle to find two 30° angles and a 120° angle for each of these similar triangles.
      120° 30° 30° 30°
    • Is ABC similar to AEF? A E F C B Sometimes it helps to separate the two triangles and look at each angle separately.
    • Find the missing side
      • We previously determined that these triangles are similar . We can set up ratios to find the missing side.
      • Start with a label on top and bottom.
      120° 30° 30° 30° 7 ft 21 ft 28 ft n ft
    • In today’s lesson…
      • We found that congruent triangles have both congruent angles and sides.
      • Similar triangles have congruent angles.
      • We can use the AA similarity to determine if triangles are similar.
      • We can use ratios to determine a missing side’s length when similar triangles are used.
      WA State Standards: G.3.A and G.3.B
    • Assign: 453: 4-8; 12-13 457: 1-4
      • This statue can be seen in downtown Seattle in the Pacific Place Mall on the main level.
    • Day Two
      • Yesterday, we found that….
      • We found that congruent triangles have both congruent angles and sides.
      • Similar triangles have congruent angles.
      • We can use the AA similarity to determine if triangles are similar.
      • Today’s Focus- Prove that triangles are similar.
    • Overlapping Triangles
      • It is sometimes useful to redraw as separate triangles to name the congruent sides and angles of those triangles.
      A C B A F E
    • Is ABC similar to AEF? If so, what Is the missing side? y 15 16 x 12 12 A B C E F
    • It often helps to separate the two attached triangles. y 15 16 x 12 12
    • Prove: A line drawn from a point on one side of a triangle parallel to another side forms a triangle similar to the original triangle.
      • Did you notice that the words corresponding occur with parallel lines and triangles?
      • Corresponding Angles in triangles are different than when working with parallel lines, but in both cases are congruent.
      WARNING
    • Given: ; Prove:
      • 1.
      • 2.
      • 3.
      • Given
      • If two || lines are intersected by a transversal, then corresponding angles are = in measure
      • AA Similarity
    • 9. Given: Prove:
      • 1.
      • 2.
      • 3.
      • 1.Given
      • 2.Alternate Interior Angles from Transversal/Parallel Lines Theorem
      • 3.AA Similarity Postulate
      A E D B C
    • Overlapping Similar Triangles Theorem
      • If a line is drawn from a point on one side of a triangle parallel to another side,
      • …then it forms a triangle similar to the original triangle.
    • Solve by using proportions 4 ft 6 ft 5 ft x
    • Assign: 453: 9; 14, 16, 21a, 23, 26 457: 5-7