Triangle Congruencies
This is a method for proving that two triangles are congruent if two sides and the included angle are equal.
What is the Side-Angle-Side (SAS) congruence theorem?
The sum of angles in any triangle always adds up to this many degrees.
What is 180 degrees?
Two triangles are similar if their corresponding angles are this.
What are equal?
The theorem stating that the square of the hypotenuse is equal to the sum of the squares of the other two sides in a right triangle.
What is the Pythagorean Theorem?
This tool often uses congruent triangles to maintain the same width between its two sides.
What is a pair of compasses?
This postulate states that two triangles are congruent if three sides of one triangle are equal to three sides of another triangle.
What is the Side-Side-Side (SSS) congruence postulate?
This is the longest side in a right triangle, opposite the right angle.
What is the hypotenuse?
Similar triangles have sides that maintain this kind of ratio.
What is proportional?
This theorem states that if one side of a triangle is longer than another, then the angle opposite the longer side is larger.
What is the Triangle Inequality Theorem?
In architecture, congruent triangles are used for this structure, known for its strength and rigidity.
What is a truss?
This condition for triangle congruence is based on the equivalence of two angles and the included side.
What is the Angle-Side-Angle (ASA) congruence postulate?
The type of triangle where two sides are equal and the base angles are also equal.
What is an isosceles triangle?
This theorem states that if a line parallel to one side of a triangle intersects the other two sides, it divides them proportionally.
What is the Triangle Proportionality Theorem?
The external angle of a triangle is equal to the sum of the opposite interior angles. Name this theorem.
What is the Exterior Angle Theorem?
Congruent triangles can ensure accurate measurements for this type of land area mapping.
What is surveying?
A shortcut for proving congruence where two angles and a non-included side are equal in two triangles.
What is the Angle-Angle-Side (AAS) congruence theorem?
These are triangles that have all three sides of different lengths.
What is a scalene triangle?
This is the type of similarity that requires only one pair of corresponding angles to be equal.
What is Angle-Angle (AA) similarity?
This theorem assures that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
What is the Triangle Inequality Theorem?
These two triangle congruency methods are used interchangeably when solving problems involving right triangles.
What are SAS and SSA?
In right triangles, this method involves the hypotenuse and one leg being congruent.
What is the Hypotenuse-Leg (HL) theorem?
The point where the three medians of a triangle intersect, often considered its center of balance.
What is the centroid?
This postulate can be used to show similarity if an angle of one triangle is congruent to an angle of another and the sides including these angles are in proportion.
What is the Side-Angle-Side (SAS) similarity postulate?
This theorem provides a formula for calculating the area of a triangle when the length of each side is known.
What is Heron's Theorem?
When constructing a parallel line through a given point with a straightedge and compass, this triangle congruency process is often applied.
What is the method of producing congruent corresponding angles?