Triangle Congruencies
This is a method for proving that two triangles are congruent if two sides and the included angle are equal.
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.
Equal?
If all three sides are equal in both triangles, what can we conclude?
.
Answer: The triangles are congruent by SSS
If the scale factor is 4 and the original side is 5 cm, what is the new length?
Answer: 20 cm?
This postulate states that two triangles are congruent if three sides of one triangle are equal to three sides of another triangle.
Side-Side-Side (SSS) congruence postulate?
This is the longest side in a right triangle, opposite the right angle.
The hypotenuse?
Similar triangles have sides that maintain this kind of ratio.
Proportional?
If two triangles have congruent angles but different side lengths, are they congruent or similar?
Answer: They are similar.
If two similar triangles have a scale factor of 1/2, what happens to the side lengths?
Answer: They are cut in half.
This condition for triangle congruence is based on the equivalence of two angles and the included side.
Angle-Side-Angle (ASA) congruence postulate?
The type of triangle where two sides are equal and the base angles are also equal.
An isosceles triangle?
If two triangles have the same shape but different sizes, what are they called?
Answer: similar triangles?
If Triangle ABC ≅ Triangle DEF, what does the symbol ≅ mean?
Answer: It means congruent.
If corresponding sides are 6 and 9, what is the scale factor from small to large?
3/2 or 1.5?
A shortcut for proving congruence where two angles and a non-included side are equal in two triangles.
Angle-Angle-Side (AAS) congruence theorem?
These are triangles that have all three sides of different lengths.
A scalene triangle?
This is the type of similarity that requires only one pair of corresponding angles to be equal.
Angle-Angle (AA) similarity?
If Triangle ABC ~ Triangle DEF, what does the symbol ~ mean?
Answer: It means similar.
If the scale factor is 3, how does the perimeter change?
Answer: It becomes 3 times larger.
In right triangles, this method involves the hypotenuse and one leg being congruent.
Hypotenuse-Leg (HL) theorem?
The point where the three medians of a triangle intersect, often considered its center of balance.
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.
Side-Angle-Side (SAS) similarity postulate?
When proving triangles congruent, why must we match corresponding parts in order?
Answer: To ensure correct corresponding sides and angles match.
Answer: To ensure correct corresponding sides and angles match.
If the scale factor is 3, how does the volume change?
Answer: It becomes 27 times larger.