The Greatest Chapter 4 Review Booklet/Online Magazine Ever!!!
By Hunter Kempton
Chapter 4 Review
You can classify a triangle to either right, acute, obtuse, or equiangular by the degree of the interior angles that make it up. The sum of the measures of the interior angles of a triangle always measures up to be 180 degrees, which is stated by the angle-sum theorem
If one of the angles is 90 degrees, it is a right triangle.
If one of the angles is more than 90 degrees, it’s an obtuse triangle.
If all of the angles are less than 90 degrees, it’s an acute triangle.
If all of the angles are 60 degrees, it’s an equiangular triangle.
The Acute angles of a right triangle are complimentary, so they add up to 90 degrees. In any triangle, there can be only one right triangle, or one obtuse triangle.
_______________________________________________________________________ _ You can also classify triangles by the measure of their sides. They can either be scalene, isosceles, or equilateral.
If none of the sides are equivalent, than it is scalene.
If 2 of the sides are equivalent, than it is isosceles.
If all of the sides are equivalent, than it is an equilateral. _______________________________________________________________________ _ Equilateral triangles are equiangular, and vice versa. You can also classify a triangle when its graphed by using the distance formula between each point to find the measure of each side. External Angles are formed by one side of a triangle and the extension of that side.
The Interior angle with the corresponding exterior angle make a straight line that is 180 degrees.
The Exterior Angle Sum Theorem states that the measure of an exterior angle is the sum of the two remote interior angles. _______________________________________________________________________ _
Triangles are congruent if, and only if, their corresponding sides and angle measures are congruent.
There are 4 main ways to prove the congruence of triangles
1. Side-Side-Side Postulate: If 3 sides of a triangle are congruent to 3 sides of another
triangle, then the triangles are congruent.
2. Side-Angle-Side Postulate: If 2 sides of a triangle are congruent to 2 corresponding angles of another triangle, and the involved angles are congruent, then the triangles are congruent.
3. Angle-Side-Angle Postulate: If 2 angles of a triangle and the included sides are congruent to the 2 angles and included sides of another triangle, the triangles are congruent.
4. Angle-Angle-Side Postulate: If 2 angles and their non-included sides are congruent to 2 angles and their non-included sides of another triangle, then the triangles are congruent.
_______________________________________________________________________ _ There are also 4 other ways to prove right triangles are congruent
1. Hypotenuse-Leg Theorem: If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, the triangles are congruent.
2. Leg-Angle Theorem: If a leg and an angle (not including the right angle) of a right triangle are congruent to a leg and an angle of another triangle, those triangles are congruent.
3. Leg-Leg Theorem: If both legs of a right triangle are congruent with the legs of another right triangle, then those triangles are congruent.
4. Hypotenuse-Angle Theorem: If the hypotenuse and one angle (not including the right angle) of a right triangle are congruent with the hypotenuse and angle of another triangle, those triangles are congruent.
By definition, isosceles triangles have 2 congruent sides called legs. The Isosceles Angle Theorem states that the opposite legs of an isosceles triangleâ€™s base angles are congruent.
To make a coordinate proof, first you make the origin a vertex of the triangle, then place at least one side on either the x or y axis. Try to keep the figure in the 1st quadrant when you can, and use coordinates that keep the math simple when plugging into the distance formula.