Geometry Part 2

Examine ΔABC .

Determine which of the following relationships is true.

• DE = 2AC

• m∠BCA = 2(m∠BED)

• DE || AC

• DE = AC

Tags

CCSS.HSG.SRT.B.4

. Lee's teacher gave her a picture of an angle and asked her to perform a common construction on the figure.

Lee used a compass to draw several arcs on the original angle and a nearby ray, as shown in the figure below.

To complete the construction, Lee must use a straightedge to connect the endpoint of the ray with the point where the two arcs intersect.

Which common construction is Lee performing?

• Parallel Lines

• Perpendicular Lines

• Angle Bisector

• Congruent Angles

Angie states the following:

"Given two triangles, if two pairs of corresponding sides and one pair of corresponding angles are congruent, then the triangles are congruent by Side–Angle–Side (SAS)."

Which of the following options best describes Angie's statement?

• Angie is correct since SAS requires two pairs of congruent sides and one pair of congruent angles.

• Angie is incorrect since SAS is not a congruence criterion that can be used to prove that two triangles are congruent

• Angie is correct since any two pairs of congruent sides and any pair of congruent angles will satisfy the SAS congruence criterion

• Angie is incorrect since triangles with two pairs of congruent sides and one pair of congruent angles do not necessarily meet the SAS criterion

Tags

CCSS.HSG.SRT.B.5

A line contains two distinct points, X and Y. Select each correct statemen

• Points X and Y determine one unique line.

• There are infinitely many points between points X and Y.

• The distance from X to Y is equal to the distance from Y to X.

• Any line segment that contains point X must also contain point Y.

• Line XY extends infinitely in both directions.

Tags

CCSS.HSG.CO.A.1

What is the equation of a line perpendicular to -x + 2 = y that intersects the line at ( -1.2 , 3.5 ) ?

• y = x + 2

• y = X + 5

• y = -x + 2

• y = - x + 5

The corresponding sides of triangles ABC and DEF are congruent. Which statements are always true for triangles ABC and DEF? Select all that apply.

• Triangles ABC and DEF are congruent by Side–Side–Side.

• Triangles ABC and DEF are both equilateral triangles by Side–Side–Side.

• There is a sequence of rigid motions that carries triangle ABC to triangle DEF.

• Triangles ABC and DEF have corresponding angles that are congruent.

• There is a sequence of dilations that carries triangle ABC onto triangle DEF.

Tags

CCSS.HSG.CO.B.7

• I and III

• II and IV

• II and III

• I and IV

Tags

CCSS.HSG.CO.C.9

• reflection over the y-axis

• dilation of scale factor -1/4

• counterclockwise rotation of 90° about the origin

• translation of 5 units to the right and 3 units down

Tags

CCSS.HSG.CO.A.2

Two rectangles are shown on the coordinate plane.

Jose claims that the two rectangles are congruent. Which of the following statements could he use to prove his claim? Select all that apply.

• The rectangles are congruent since a translation of 6 units down and 7 units to the left carries Rectangle 1 onto Rectangle 2.

• The rectangles are congruent since a reflection over the x–axis followed by a translation of 7 units to the right carries Rectangle 1 onto Rectangle 2.

• The rectangles are congruent since a reflection over the y–axis followed by a translation of 1 unit to the right and 6 units up carries Rectangle 1 onto Rectangle 2.

• The rectangles are congruent since a rotation of 180° clockwise about the origin followed by a translation of 1 unit to the right carries Rectangle 1 onto Rectangle 2

• The rectangles are congruent since a reflection over the x–axis followed by a translation of 5 units to the right carries Rectangle 1 onto Rectangle 2.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

• A

• B

• C

• D

Tags

CCSS.HSG.CO.A.2