Triangle Similarity
Which of these is NOT a triangle similarity theorem? ASA, SAS, SSS, AA
ASA
A midsegment of a triangle is a segment connecting the ________ of two of its sides.
midpoints
It is not possible to draw a triangle with a third side that is greater than the _____ of the other two sides.
sum
If you draw a segment directly from the vertex of a triangle to the midpoint of the opposite side, you have drawn a _____.
median
What does CPCTC stand for?
Corresponding parts of congruent triangles are congruent.
Triangle BAC is similar to triangle PQR. If angle C is 39 degrees, angle R must be how many degrees?
39 degrees
DAILY DOUBLE!! DAILY DOUBLE!!!
Triangle ABC has a midsegment XY that connects the midpoints of side AB and side BC. Which side of triangle ABC is parallel to midsegment XY?
CA
For triangle XYZ, the length of side YZ + the length of side ZX will always be greater than the length of...
side XY
How many medians does each triangle have?
3
The incenter of a triangle is the point of concurrency formed by the intersection of three _____ _______.
angle bisectors
You are told that two isosceles triangles are similar. If the legs of the first triangle are 5 cm., the base of the first triangle is 3 cm., and the base of the second triangle is 9 cm., how long are the legs of the second triangle?
15 cm.
Triangle ZAM has a midsegment EW that connects the midpoints of AM and MZ. Midsegment EW is 1/2 the length of which of the sides of triangle ZAM?
ZA
Triangle RUT has side lengths RU=5 cm. and UT=7 cm. Triangle SAY has side lengths SA=5 cm. and AY=7 cm. Angle U is 43 degrees, while angle A is 39 degrees. Which side is longer: side TR or side YS?
side TR
The length from the centroid to the midpoint of the side of any triangle is ___ the length from the vertex to the centroid.
Triangle VIN has the following side lengths: VI=8 cm., IN=23 cm., and NV=17 cm. Triangle MOE has the following side lengths: MO=32 cm., OE=82 cm., and EM=68 cm. If you wanted to change a single side length on triangle MOE to make these triangles similar, which side length would you change?
OE (change 82 cm. to 92 cm.)
Triangle CAT is similar to triangle DOG. If angle A is 47 degrees, the sum of angle D and G must be how many degrees?
133 degrees
Triangle QRS has a midsegment OP that is parallel to side RS. If the length of midsegment OP is 30 cm., what is the sum of midsegment OP and side RS?
90 cm.
Triangle FGH has side lengths FG=14 cm. and GH=9 cm. What is the range of possible side lengths for side HF? (In other words, what two values does the side length have to be between?)
5 cm. < x < 23 cm.
If you drew all possible medians of a certain triangle, the triangle would be divided up into ___ smaller triangles.
6
The point of concurrency of the perpendicular bisectors of a triangle, or the circumcenter, is equidistant to the _____ of the triangle.
vertices
Triangle CTP and triangle JMK are similar triangles. Angle J is 64 degrees. Angle K is 37 degrees. Line segment PC is 75 mm. Triangle CTP is four times smaller than triangle JMK. What is the length of line segment KJ?
300 mm.
Triangle TOY has a midsegment VR that connects the midpoints of side TO and side OY. If midsegment VR has a length of x+4 and side YT has a length of 3x-2, what is the value of x?
x=10
Victor draws a triangle QWE with side lengths WE=45 and EQ=35. In his triangle, angle E is 68 degrees. Kaleb draws a triangle IOP with side lengths PI=35 and OP=45. In his triangle, angle P is 87 degrees. If the third side of Victor's triangle has a side length QW=3x+8 and the third side of Kaleb's triangle has a side length IO=44, the value of x cannot be greater than...
12
Triangle ASD has medians ZS, XD, and CA. L is the centroid of the triangle. If ZS=3 cm., XD=5 cm., and CA=2 cm., what is the length of SL?
2 cm.
Triangle IOP has medians JO, KP, and LI. A is the centroid of the triangle. If JO=3 cm., KP=5 cm., and LI=2 cm., what is the length of JA?
1 cm.