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