Angle Relationships Answers
The Angle-Side Relationship states that In a triangle, the side opposite the larger angle is the longer side. In a triangle, the angle opposite the longer side is the larger angle. In a triangle, if the second angle is 5° greater than the first angle and the third angle is 5° greater than second angle, find the three angles of the triangle. Before talking about Geometry Angle Relationships Worksheet Answers, please are aware that Instruction is actually all of our crucial for a much better down the road, and also understanding won’t just quit after a institution bell rings.That will staying explained, most of us supply you with a a number of basic yet enlightening articles or blog posts as well as design templates built suited.
More Geometry LessonsIn these lessons, we will learn two commonly used inequality relationships in a triangle:
- the Triangle Inequality Theorem
- the Converse of the Triangle Inequality Theorem
- the Angle-Side Relationship for triangles
Triangle Inequality Theorem
The Triangle Inequality theorem states that
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
The Converse of the Triangle Inequality theorem states that
It is not possible to construct a triangle from three line segments if any of them is longer than the sum of the other two.
Example 1:Angle Relationships Edgenuity Answers
Find the range of values for s for the given triangle.Solution:
Step1: Using the triangle inequality theorem for the above triangle gives us three statements:
s + 4 > 7 ⇒ s > 3
s + 7 > 4 ⇒ s > –3 (not valid because lengths of sides must be positive)
7 + 4 > s ⇒ s < 11
Step 2: Combining the two valid statements:
3 < s < 11
Answer: The length of s is greater than 3 and less than 11
The following video states and investigates the triangle inequality theorem.
The sum of lengths of any two sides of a triangle must be greater than the length of the third.
We really only need to make sure the sum of the lengths of the two shorter sides is greater than the length of the longest side.
Examples:
Angle Relationships Answers
Which lengths can form a triangle?
1. 3, 4, 6
2. 5, 6, 11
3. 2, 3, 9
- Show Step-by-step Solutions
The following video describes triangle inequality by trying to construct triangles with different length segments. What are the conditions required to draw a triangle to illustrate triangle inequality?
- Show Step-by-step Solutions
Angle-Side Relationship
The Angle-Side Relationship states that
In a triangle, the side opposite the larger angle is the longer side.
In a triangle, the angle opposite the longer side is the larger angle.
Example 1: Compare the lengths of the sides of the following triangle.
Solution:
Step1: We need to find the size of the third angle. The sum of all the angles in any triangle is 180º.
∠A + ∠B + ∠C = 180°
⇒ ∠A + 30° + 65° = 180°
⇒ ∠A = 180° - 95°
⇒ ∠A = 85°
Step 2: Looking at the relative sizes of the angles.
∠B < ∠C < ∠A
Step 3: Following the angle-side relationship we can order the sides accordingly. Remember it is the side opposite the angle.
Answer:
Examples of the angle-side relationships in triangles- Show Step-by-step Solutions
If 2 sides of a triangle are not congruent, then the larger angle is opposite the larger side.
If 2 angles of a triangle are not congruent, then the larger side is opposite the larger angle.
The measure of Angle A is greater than the measure of Angle B, and the measure of Angle B is greater than the measure of Angle C. Find the possible values for the length of side AC.
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