Table of Contents
- 1 What kind of triangle has two congruent sides and two congruent angles?
- 2 What is the AAA congruence theorem?
- 3 What kind of triangle has 2 congruent sides?
- 4 Can a triangle have 2 congruent angles?
- 5 What is SSS triangle?
- 6 What is SAS triangle?
- 7 Which is the included side of a triangle?
- 8 What does the AAS theorem say about a triangle?
What kind of triangle has two congruent sides and two congruent angles?
Isosceles triangle: two congruent sides and two congruent angles (two sides of equal length and two angles of equal measure).
What is the AAA congruence theorem?
may be reformulated as the AAA (angle-angle-angle) similarity theorem: two triangles have their corresponding angles equal if and only if their corresponding sides are proportional.
What is SSS SAS ASA and AAS congruence?
SSS (side-side-side) All three corresponding sides are congruent. SAS (side-angle-side) Two sides and the angle between them are congruent. ASA (angle-side-angle)
What is SSS SAS ASA AAS?
SSS stands for “side, side, side” and means that we have two triangles with all three sides equal. If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent. SAS (side, angle, side)
What kind of triangle has 2 congruent sides?
Scalene triangle: A triangle with no congruent sides. Isosceles triangle: A triangle with at least two congruent sides. Equilateral triangle: A triangle with three congruent sides.
Can a triangle have 2 congruent angles?
Triangles can be classified by their angle measures and side lengths. For triangles only, equiangular and equilateral have the same implications: all sides and angles are congruent. Isosceles triangles have at least two congruent sides and two congruent angles.
What is HL triangle?
The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent. Hypotenuse Theorem Example.
What is a AAS triangle?
4. AAS (angle, angle, side) AAS stands for “angle, angle, side” and means that we have two triangles where we know two angles and the non-included side are equal.
What is SSS triangle?
When two triangles are congruent, all three pairs of corresponding sides are congruent and all three pairs of corresponding angles are congruent. This congruence shortcut is known as side-side-side (SSS).
What is SAS triangle?
If we can show that two sides and the included angle of one triangle are congruent to two sides and the included angle in a second triangle, then the two triangles are congruent. This is called the Side Angle Side Postulate or SAS.
Which triangle has congruent angles?
Equilateral triangles have interior angles that are all congruent so they are equiangular.
When are two angles of a triangle congruent?
If two angles and their included side of one triangle are all congruent to two corresponding angles and their included side of another triangle, the two triangles are congruent. Here we offer two new triangles, △ LEG △ L E G and △ ARM △ A R M. Notice all the little hatch marks indicating congruent angles and sides:
Which is the included side of a triangle?
An included angle or side is physically between the others in the triangle. So Side Angle Side (SAS) means one side, the angle next to that side, and then the side next to that angle. That side is out there, all alone, not between the angles. For every testing method, you are checking the three parts identified between the two triangles.
What does the AAS theorem say about a triangle?
The AAS Theorem says: If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. Notice how it says “non-included side,” meaning you take two consecutive angles and then move on to the next side (in either direction).
Can you find a congruence proof for angle angle side?
Notice, for instance, you cannot find Angle Angle Angle as a congruence proof (that is reserved for similarity), nor can you cook up a Side Side Angle postulate. Whichever term you see sandwiched between the others, that part is included.