Blog

(01.03 MC) Layla is using her compass and straightedge to complete construction of a polygon inscribed in a circle. Which polygon is she in the process of constructing?

(02.04 MC) ABC is a right triangle. Point D is the midpoint of side AB, and point E is the midpoint of side AC. The measure of angle ADE is 47°. The following flowchart with missing statements and reasons proves that the measure of angle ECB is 43°: Which statement and reason can be used to fill in the numbered blank spaces?

(02.06 MC) Figure ABCD is a rhombus, and m∠AEB = 7x + 6. Solve for x.

(02.01 HC) Triangle END is reflected across the line y = x using the rule (x, y) → (y, x) to create triangle E′N′D′. If a line segment is drawn from point E to point E′, which statement would best describe the line segment drawn in relation to the line y = x?

(03.01 LC) is dilated from the origin to create at D′ (0, 3) and F′ (2.25, 1.5). What scale factor was dilated by?

(02.03 MC) Angle N = 40 degrees, side NP = 8, angle Q = 40 degrees, and side QS = 8. What additional information would you need to prove that ΔNOP ≅ ΔQRS by ASA?

(02.03 MC) Peter reflected trapezoid ABCD across the y-axis. If angle A is 115° and angle B is 65°, what is the degree measurement of angle A′?

(02.03 MC) Triangle HIJ has been reflected to create triangle H′I′J′. Segment HJ = H′J′ = 4, segment IJ = I′J′ = 7, and angles J and J′ are both 32 degrees. Which postulate below would prove the two triangles are congruent?

(02.04 HC) C is the circumcenter of isosceles triangle ABD with vertex angle ∠ABD. Does the following proof correctly justify that triangles ABE and DBE are congruent? It is given that triangle ABD is an isosceles triangle, so segments AB and DB are congruent by the definition of isosceles triangle. It is given that C is the circumcenter of triangle ABD, making segment BE a median. By the definition of perpendicular, angles AEB and DEB are 90°, so triangles ABE and DEB are right triangles. Triangles ABE and DEB share side BE making it congruent to itself by the reflexive property. Triangles ABE and DBE are congruent by HL.

(02.01 HC) Triangle JOY is translated using the rule (x, y) → (x + 3, y − 2) to create triangle J′O′Y′. If a line segment is drawn from point J to point J′ and from point O to point O′, which statement would best describe the line segments drawn in relation to one another?