Unit Six: Similarity; Triangle Theorems
Use the given information to match the answers. ABC is a right triangle. 1. 2 root 13 2. root 5 3. 3 root 3 If a = 4 and b = 6, then c = If a = 3 and c = 6, then b = If b = 2 and c = 3, then a =
1. If a = 4 and b = 6, then c = 2. If b = 2 and c = 3, then a = 3. If a = 3 and c = 6, then b =
Triangle RST is an equilateral triangle; Segment TX is perpendicular to Segment RS. If TX = 6 then RX = 3 2√3 6√3 12
2 root 3
In triangle RST, Segment XY is parallel to Segment RS If TX = 3, XR = TY, and YS = 6, find XR. 3√3 4√3 √5 3√2
3√2
Triangle RST is an equilateral triangle; Segment TX is perpendicular to Segment RS. If RT = 8, then TX = 3√3 4√3 √5 3√2
4 root 3
Given Angle 1 = Angle 2, find x.
6
Triangle RST is an equilateral triangle; Segment TX is perpendicular to Segment RS. If RX = 3, then RT = 1.5 3√2 3√3 6
6
Using the Pythagorean Theorem, which of the triangles shown are right triangles? A B C
A
If three corresponding sides of one triangle are proportional to three sides of another, then the triangles are similar. always sometimes never
Always
The angles of similar triangles are equal. always sometimes never
Always
The slant height of a regular square pyramid is longer than its altitude. always sometimes never
Always
True/False - In a 30-60-90 triangle, the hypotenuse is the shorter leg times the square root of two.
False
All of the following are pairs of corresponding sides in similar triangles except RS and RT RX and TX RX and SX XS and TS
RX and SX
In triangle RST, RT = 4, ST = 8, and Segment TX bisects angle RTS. Which of the following proportions must be true? RX/ST = TR/XS TX/XR = ST/RT RX/RT = SX/ST RX/RS = XS/ST
RX/RT = SX/ST
A line that passes through two sides of a triangle divides the sides proportionally. always sometimes never
Sometimes
If the lengths of corresponding altitudes have the same ratio as the length of any pair of corresponding sides, the two triangles are similar. always sometimes never
Sometimes
Similar triangles are congruent. always sometimes never
Sometimes
True/False - A line parallel to one side of a triangle, and intersects the other two sides, divides the other two sides proportionally.
True
True/False - If two sides of one triangle are proportional to two sides of another and included angles are equal, then the triangles are similar.
True
True/False - The perimeters of similar triangles are in the same ratio as the corresponding sides.
True
Find the missing part.
x = 2 root 41