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Similar Polygons
Circles
Coordinate Geometry
Triangles
100
Which of the following is not preserved under a dilation? A.) Angle Measure; B.) Collinearity; C.) Distance; D.) Orientation
C.) Distance
100
Chords AB and CD are parallel in a circle. If AB is a diameter, and the measure of arc AC = 40 degrees, then the measure of arc CD is A.) 180; B.) 40; C.) 100; D.) 60
C.) 100 degrees
100
Point T(2,-3 ) & Point S(1, -5). What are the coordinates of point M, the midpoint of TS?
Midpoint: [ (x1 + x2) / 2 , (y1+y2)/2 ]; Answer: M(1.5, -4 )
100
The lengths of the sides of a triangle could be: A.) 4, 5, 8; B.) 16, 20, 40; C.) 2, 3, 5; D.) 1, 1, 3
A.) 4,5,8. Triangle Inequality Theorem. The sum of any two sides must be greater than the third side. 4 + 5 > 8.
200
In Triangle ABC, D is the midpoint of side AB and E is the midpoint of AC. DE is drawn. If DE = 15, DB = 6, and AD = 10, what is the length of side BC?
Proportion: 10:15 = 16:x; 10x = 240 ; Answer: BC = 24
200
Point P has its vertex outside the circle, and a secant and tangent line are drawn from external point P. to find the measure of angle P you would
Subtract the 2 intercepted arcs and divide by 2
200
Point D(-2,-3) and Point E(4, -6 ). What is the length of line segment DE?
Distance Formula: Sqrt of [( x2-x1)^2 + ( y2 - y1)^2 ]; Sqrt of { (6)^2 + (-3)^2 } ; SQRT of ( 36 + 9 ); SQRT of 45 = 3 radical 5
200
Medians AG and BE are drawn in triangle ABC. Point E lies on side AC, and point G lies on side BC. The medians intersect at point W. If BE = 24, what is the length of BW?
W is the centroid, and it divides the medians into a 2:1 ratio. So, let BW = 2x, WE = x. ; 2x + x = 24; x = 8, so BW = 16.
300
In triangle ABC, the angle measure of angle A is 30 degrees, & the length of segment AB is 12 cm. Determine the length of A'B' & the measure angle A after a dilation D3.
Angle A = 30 degrees A'B' = 36 cm
300
Point P lies at the intersection of chord AB and CD. To find the measure of angle APC you would
add the measure of arc AC and arc DB and then divide by 2.
300
A quadrilateral has ordered pairs A(3,3) ; B(5,4); C(-4, 7); and D( 1, -3). Are AB and CD parallel, perpendicular, or neither?
Compare slopes: Slope of AB: (y2-y1)/(x2-x1) ---> 1/2; Slope of CD: 10/-5 = -2/1; Since -2/1 & 1/2 are negative reciprocals of each other, AB is perpendicualr to CD.
300
Triangle ABC, with sides AB = 6, BC = 4, and AC = 7. What is the perimeter of the triangle formed by connecting the midpoints of all the sides of triangle ABC?
Perimeter = 3 + 2 + 3.5 = 8.5
400
In triangle DEF, point A lies on side DE, and point B lies on side DF. AB is drawn and AB || EF. AD = 6, BD 10, & AE = 3. Determine the length of BF.
Proportion: 6:3 = 10:x; 6x = 30; Answer: BF = 5
400
A circle is inscribed in triangle ABC such that D,E, and F lie on sides AB, BC, and AC respectively, and points D,E,and F are points on the circle. AD, AE, and BF are all tangent lines to the circle. AD = 6, FC = 8, and BD = 9. What is the length of BC?
BC = 8 + 9 = 17. ( Tangents from the same external point are equal. )
400
Triangle ABC is graphed in the coordinate plane with A(0,4), B( 6, 4) and C(3,2). Classify the triangle by its sides. Justify your answer.
Distance formula: AB = SQRT of 36 = 6; BC = SQRT of 13; AC = SQRT of 13. Answer: Triangle ABC is isosceles.
400
Del draws a triangle with side lengths of 0.8, 1.7, and 1.5 cm. Is the triangle a right triangle? Justify your answer.
Yes, by the pythagorean theorem. (0.8)^2 + (1.5)^2 = (1.7)^2
500
Which of the following is not a valid method of proving two triangles are similar? A.) SSS ; B.) SAS ; C.) AA ; D.) HL
D.) HL
500
Two secants are drawn from point P. The first secant, PAB, PA = 5, and AB = 15. The other secant, PCD, PC = 4. What is the measure of CD?
(Whole secant )x (external piece) = (whole secant x external piece) ; (PA + AB )( PA ) = ( PC + CD )(PC); (5 + 15 )(5) = ( 4 + x )(4) ; 100 = 4x + 16; 4x = 84; Answer: x = 21
500
Write the equation of a line perpendicular to 3y - 2x = 6, and passes through the point (-6, 2 ).
Slope of given line is 2/3 when you move the x and then divide. Perpendicular slope = -3/2. Substitute in y=mx+b; 2 = -3/2(-6) + b; b = -7. Answer: Equation is y = -3/2x - 7.
500
Triangle ABC has angle A measuring 43 degrees, and angle B measures 65 degrees. What is the largest side of triangle ABC?
Angle C measures 72 degrees, and is the largest angle. Answer: AB is the largest side b/c it is opposite the largest angle.