Triangle Congruence Postulates
This postulate states that two triangles are congruent if all three pairs of corresponding sides are equal.
What is the Side-Side-Side (SSS) Postulate?
Congruent triangles have all corresponding angles and sides equal. This property is sometimes called ‘CPCTC.’
What is Corresponding Parts of Congruent Triangles are Congruent?
A proof involving congruent triangles often begins with this type of statement to establish relationships between elements.
What is a given statement?
In real-world scenarios, congruent triangles can be used directly to ensure the accuracy of this type of art involving geometric shapes.
What is tessellation or tiling?
This special type of triangle has two sides equal, making it one of the initial types to check for congruence properties.
What is an isosceles triangle?
This postulate states that two triangles are congruent when two sides and the angle between them are equal.
What is the Side-Angle-Side (SAS) Postulate?
If a triangle is an equilateral triangle it is also a ____________ triangle.
What is a equiangular?
When proving congruence of triangles, this type of reasoning is often utilized to deduce properties logically from known facts.
What is deductive reasoning?
Architects use congruent triangles to assure this quality in bridge design, ensuring equal weight distribution and stability.
What is structural integrity?
Formed by dividing an equilateral triangle, each of the resulting triangles are identical and maintain this property.
What is being congruent?
This congruence criterion is used when two angles and the side between them are known.
What is the Angle-Side-Angle (ASA) Postulate?
Two overlapping triangles in a diagram can often be proven congruent by identifying this shared element as part of their congruence.
What is a shared side or overlap?
In a proof, this step comes after identifying your given and looking for shared sides or angles to assist your argument.
What is proving congruence using a postulate or theorem?
Surveyors often rely on congruent triangles to accurately determine the distance across this kind of open space or geographic expanse.
What is a river or valley?
In a right triangle, if two other triangles formed from the altitude to the hypotenuse are congruent to the entire triangle, these shapes are called what?
What are similar shapes or similar triangles?
This criterion uses two angles and a non-included side to prove congruence.
What is the Angle-Angle-Side (AAS) Theorem?
If two triangles are congruent, then their sides and these measurements are also equal.
What are their angles?
When you prove two triangles congruent, this theorem is often used afterwards to show further equalities in other geometric figures involving these triangles.
What is Corresponding Parts of Congruent Triangles are Congruent (CPCTC)?
Congruent triangles are key in calculating these angular measurements in the field of aviation and science for accurate navigation.
What are angles of elevation or depression?
What are angles of elevation or depression?
If triangle ABC is congruent to triangle DEF, there are ______ side congruencies and ______ angle congruencies.
What are 3 sides and 3 angles?
This postulate applies in right triangles when the hypotenuse and one leg are known to be equal in both triangles.
What is the Hypotenuse-Leg (HL) Theorem?
In proving congruent triangles, this 'no choice' theorem implies that equilateral triangles automatically have all corresponding angles equal, which equals how many degrees?
What is 60 degrees?
This concept involves using a chain of reasoning where one pair of triangles' congruency implies another, often linked through transitive properties.
What is transitive property in congruence?
In robotics, ensuring moving parts are congruent triangles helps achieve these consistent and precise movements.
What are rotational movements or maneuvers?
If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
What is the Converse of the Isosceles Triangle Theorem?