Similarity Criteria (AA, SSS, SAS)
If two angles in one triangle are congruent to two angles in another, the triangles are similar by this postulate.
(What is AA/Angle-Angle?)
A comparison of two quantities, often written as a:b or a/b
(What is a ratio?)
This theorem states that a line parallel to one side of a triangle divides the other two sides proportionally.
(What is the Triangle Proportionality Theorem?)
Similar figures have the same shape but different sizes, and their corresponding angles must be this.
(What is congruent?)
Solve for (x) given the proportion 3/4 = X/12
(What is 9?)
This criterion requires two sets of corresponding sides to be proportional and their included angles to be congruent.
(What is SAS/Side-Angle-Side?) [1, 2]
If the scale factor from Triangle A to Triangle B is 2:3, and Triangle A's perimeter is (18) inches, this is the perimeter of Triangle B.
(What is 27 inches?)
When an angle of a triangle is bisected, it divides the opposite side into two segments that are proportional to these.
(What are the adjacent sides?)
In similar polygons, corresponding sides are not equal, but they are this.
(What is proportional?)
If (triangle) ABC ~ (triangle) DEF, (AB = 5), \(BC = 7), and (DE = 15), solve for the length of (EF).
(What is 21?)
True or False: You can use the Angle-Angle-Angle (AAA) theorem to prove two triangles are similar.
(What is False?)
The ratio of the areas of two similar triangles is always the square of this value.
(What is the scale factor?) [1]
If three or more parallel lines intersect two transversals, then they cut off the transversals.
(What are proportionally?)
This property states that any triangle is similar or congruent to itself.
(What is the Reflexive Property?)
Given (triangle) MNP ~ (triangle) RST, (MN = x + 3), \(RS = 2x), (MP = 12), and(RT = 16). Solve for (x).
(What is 6?)
To prove triangles similar by this theorem, all corresponding sides must form a constant ratio.
(What is SSS/Side-Side-Side?) [1, 2]
If (Triangle) XYZ ~ (Triangle) ABC and XY/AB = 4/5, this is the value of the ratio YZ/BC
(What is 4/5 ?)
If segment (DE) connects the midpoints of sides (AB) and (AC), this is the relationship between the lengths of (DE) and (BC).
(What is (DE) is half the length of (BC)?)
In the similarity statement (Triangle) JKL ~ (Triangle) MNO, his is the side that corresponds to side (KL).
What is side (NO)?
In (triangle) ABC, line (DE) is parallel to side (BC). (AD = 4), (DB = 2), and (AE = 6). Solve for the length of (EC).
(What is 3?)
Identify the minimal similarity criterion required to prove two right triangles similar if one acute angle in each is known to be 45 degree
(What is AA?)
The sides of a triangle measure (6), (8), and (10). If the shortest side of a similar triangle is (15), this is the perimeter of the larger triangle.
(What is 60?)
A theorem that allows you to calculate the height of a tree by using a shadow cast by a person of known height.
(What is the AA Similarity Theorem?)
This is the ratio used to compare the lengths of the corresponding sides of two similar figures.
(What is the scale factor?)
Solve for (x) given the overlapping similar triangles: (triangle) ADE is situated within (triangle) ABC. (AD = x), (DB = 3), (AE = 6), and (EC = 2)
(What is 9?)