4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths...
Transcript of 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths...
![Page 1: 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths of equilateral FGH. Check It Out! Example 3 Step 1 Find the value of y. Given.](https://reader035.fdocuments.net/reader035/viewer/2022071214/6041d24905b46f6c186c2a92/html5/thumbnails/1.jpg)
Holt McDougal Geometry
4-2 Classifying Triangles
Bellringer:
Classify each angle as acute, obtuse, or right.
1. 2.
3.
4. If the perimeter is 47, find x and the lengths
of the three sides.
rightacute
x = 5; 8; 16; 23
obtuse
![Page 2: 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths of equilateral FGH. Check It Out! Example 3 Step 1 Find the value of y. Given.](https://reader035.fdocuments.net/reader035/viewer/2022071214/6041d24905b46f6c186c2a92/html5/thumbnails/2.jpg)
Holt McDougal Geometry
4-2 Classifying Triangles
Classify triangles by their angle measures and side lengths.
Use triangle classification to find angle
measures and side lengths.
Objectives
![Page 3: 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths of equilateral FGH. Check It Out! Example 3 Step 1 Find the value of y. Given.](https://reader035.fdocuments.net/reader035/viewer/2022071214/6041d24905b46f6c186c2a92/html5/thumbnails/3.jpg)
Holt McDougal Geometry
4-2 Classifying Triangles
acute triangle
equiangular triangle
right triangle
obtuse triangle
equilateral triangle
isosceles triangle
scalene triangle
Vocabulary
![Page 4: 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths of equilateral FGH. Check It Out! Example 3 Step 1 Find the value of y. Given.](https://reader035.fdocuments.net/reader035/viewer/2022071214/6041d24905b46f6c186c2a92/html5/thumbnails/4.jpg)
Holt McDougal Geometry
4-2 Classifying Triangles
Recall that a triangle ( ) is a polygon with three sides. Triangles can be classified in two ways: by their angle measures or by their side lengths.
![Page 5: 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths of equilateral FGH. Check It Out! Example 3 Step 1 Find the value of y. Given.](https://reader035.fdocuments.net/reader035/viewer/2022071214/6041d24905b46f6c186c2a92/html5/thumbnails/5.jpg)
Holt McDougal Geometry
4-2 Classifying Triangles
B
A
C
AB, BC, and AC are the sides of ABC.
A, B, C are the triangle's vertices.
![Page 6: 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths of equilateral FGH. Check It Out! Example 3 Step 1 Find the value of y. Given.](https://reader035.fdocuments.net/reader035/viewer/2022071214/6041d24905b46f6c186c2a92/html5/thumbnails/6.jpg)
Holt McDougal Geometry
4-2 Classifying Triangles
Acute Triangle
Three acute angles
Triangle Classification By Angle Measures
![Page 7: 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths of equilateral FGH. Check It Out! Example 3 Step 1 Find the value of y. Given.](https://reader035.fdocuments.net/reader035/viewer/2022071214/6041d24905b46f6c186c2a92/html5/thumbnails/7.jpg)
Holt McDougal Geometry
4-2 Classifying Triangles
Equiangular Triangle
Three congruent acute angles
Triangle Classification By Angle Measures
![Page 8: 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths of equilateral FGH. Check It Out! Example 3 Step 1 Find the value of y. Given.](https://reader035.fdocuments.net/reader035/viewer/2022071214/6041d24905b46f6c186c2a92/html5/thumbnails/8.jpg)
Holt McDougal Geometry
4-2 Classifying Triangles
Right Triangle
One right angle
Triangle Classification By Angle Measures
![Page 9: 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths of equilateral FGH. Check It Out! Example 3 Step 1 Find the value of y. Given.](https://reader035.fdocuments.net/reader035/viewer/2022071214/6041d24905b46f6c186c2a92/html5/thumbnails/9.jpg)
Holt McDougal Geometry
4-2 Classifying Triangles
Obtuse Triangle
One obtuse angle
Triangle Classification By Angle Measures
![Page 10: 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths of equilateral FGH. Check It Out! Example 3 Step 1 Find the value of y. Given.](https://reader035.fdocuments.net/reader035/viewer/2022071214/6041d24905b46f6c186c2a92/html5/thumbnails/10.jpg)
Holt McDougal Geometry
4-2 Classifying Triangles
Classify BDC by its angle measures.
Example 1A: Classifying Triangles by Angle Measures
![Page 11: 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths of equilateral FGH. Check It Out! Example 3 Step 1 Find the value of y. Given.](https://reader035.fdocuments.net/reader035/viewer/2022071214/6041d24905b46f6c186c2a92/html5/thumbnails/11.jpg)
Holt McDougal Geometry
4-2 Classifying Triangles
Classify ABD by its angle measures.
Example 1B: Classifying Triangles by Angle Measures
![Page 12: 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths of equilateral FGH. Check It Out! Example 3 Step 1 Find the value of y. Given.](https://reader035.fdocuments.net/reader035/viewer/2022071214/6041d24905b46f6c186c2a92/html5/thumbnails/12.jpg)
Holt McDougal Geometry
4-2 Classifying Triangles
Classify FHG by its angle measures.
Check It Out! Example 1
∠EHG is a right angle. Therefore m∠EHF +m∠FHG = 90°. By substitution, 30°+ m∠FHG = 90°. So m∠FHG = 60°.
FHG is an equiangular triangle by definition.
![Page 13: 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths of equilateral FGH. Check It Out! Example 3 Step 1 Find the value of y. Given.](https://reader035.fdocuments.net/reader035/viewer/2022071214/6041d24905b46f6c186c2a92/html5/thumbnails/13.jpg)
Holt McDougal Geometry
4-2 Classifying Triangles
Equilateral Triangle
Three congruent sides
Triangle Classification By Side Lengths
![Page 14: 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths of equilateral FGH. Check It Out! Example 3 Step 1 Find the value of y. Given.](https://reader035.fdocuments.net/reader035/viewer/2022071214/6041d24905b46f6c186c2a92/html5/thumbnails/14.jpg)
Holt McDougal Geometry
4-2 Classifying Triangles
Isosceles Triangle
At least two congruent sides
Triangle Classification By Side Lengths
![Page 15: 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths of equilateral FGH. Check It Out! Example 3 Step 1 Find the value of y. Given.](https://reader035.fdocuments.net/reader035/viewer/2022071214/6041d24905b46f6c186c2a92/html5/thumbnails/15.jpg)
Holt McDougal Geometry
4-2 Classifying Triangles
Scalene Triangle
No congruent sides
Triangle Classification By Side Lengths
![Page 16: 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths of equilateral FGH. Check It Out! Example 3 Step 1 Find the value of y. Given.](https://reader035.fdocuments.net/reader035/viewer/2022071214/6041d24905b46f6c186c2a92/html5/thumbnails/16.jpg)
Holt McDougal Geometry
4-2 Classifying Triangles
Remember!
When you look at a figure, you cannot assume segments are congruent based on appearance. They must be marked as congruent.
![Page 17: 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths of equilateral FGH. Check It Out! Example 3 Step 1 Find the value of y. Given.](https://reader035.fdocuments.net/reader035/viewer/2022071214/6041d24905b46f6c186c2a92/html5/thumbnails/17.jpg)
Holt McDougal Geometry
4-2 Classifying Triangles
Classify EHF by its side lengths.
Example 2A: Classifying Triangles by Side Lengths
![Page 18: 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths of equilateral FGH. Check It Out! Example 3 Step 1 Find the value of y. Given.](https://reader035.fdocuments.net/reader035/viewer/2022071214/6041d24905b46f6c186c2a92/html5/thumbnails/18.jpg)
Holt McDougal Geometry
4-2 Classifying Triangles
Classify EHG by its side lengths.
Example 2B: Classifying Triangles by Side Lengths
![Page 19: 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths of equilateral FGH. Check It Out! Example 3 Step 1 Find the value of y. Given.](https://reader035.fdocuments.net/reader035/viewer/2022071214/6041d24905b46f6c186c2a92/html5/thumbnails/19.jpg)
Holt McDougal Geometry
4-2 Classifying Triangles
Classify ACD by its side lengths.
Check It Out! Example 2
From the figure, . So AC = 15, and ACD is scalene.
![Page 20: 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths of equilateral FGH. Check It Out! Example 3 Step 1 Find the value of y. Given.](https://reader035.fdocuments.net/reader035/viewer/2022071214/6041d24905b46f6c186c2a92/html5/thumbnails/20.jpg)
Holt McDougal Geometry
4-2 Classifying Triangles
Find the side lengths of JKL.
Example 3: Using Triangle Classification
Step 1 Find the value of x.
![Page 21: 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths of equilateral FGH. Check It Out! Example 3 Step 1 Find the value of y. Given.](https://reader035.fdocuments.net/reader035/viewer/2022071214/6041d24905b46f6c186c2a92/html5/thumbnails/21.jpg)
Holt McDougal Geometry
4-2 Classifying Triangles
Find the side lengths of JKL.
Example 3 Continued
Step 2 Substitute the value of x into the expressions to find the side lengths.
![Page 22: 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths of equilateral FGH. Check It Out! Example 3 Step 1 Find the value of y. Given.](https://reader035.fdocuments.net/reader035/viewer/2022071214/6041d24905b46f6c186c2a92/html5/thumbnails/22.jpg)
Holt McDougal Geometry
4-2 Classifying Triangles
Find the side lengths of equilateral FGH.
Check It Out! Example 3
Step 1 Find the value of y.
Given.
FG = GH = FH Def. of ≅ segs.
3y – 4 = 2y + 3
Substitute (3y – 4) for FG and (2y + 3) for GH.
y = 7Add 4 and subtract 2y from both sides.
![Page 23: 4-2 Classifying Triangles · Holt McDougal Geometry 4-2 Classifying Triangles Find the side lengths of equilateral FGH. Check It Out! Example 3 Step 1 Find the value of y. Given.](https://reader035.fdocuments.net/reader035/viewer/2022071214/6041d24905b46f6c186c2a92/html5/thumbnails/23.jpg)
Holt McDougal Geometry
4-2 Classifying Triangles
Find the side lengths of equilateral FGH.
Check It Out! Example 3 Continued
Step 2 Substitute 7 into the expressions to find the side lengths.
FG = 3y – 4
= 3(7) – 4 = 17
GH = 2y + 3
= 2(7) + 3 = 17
FH = 5y – 18
= 5(7) – 18 = 17