Honors Geometry Entrance Assessment

Use the Converse of the Corresponding Angles Postulate and \angle1\cong\angle2 to show thatl\parallel m.

Tags

CCSS.8.G.A.5

Fill in the blanks to complete the two-column proof.

Given: ∠1 and ∠2 are supplementary and linear. m∠1 = 135°

Prove: m∠2 = 45°

• 
• 
• 
• 

Tags

CCSS.7.G.B.5

• 
• 
• 
• 

Tags

CCSS.HSG.CO.C.11

KL ≅ MN and ∠KLM ≅ ∠MNK. Determine if the quadrilateral must be a parallelogram. Justify youranswer.

• No. Only one set of angles and sides are given as congruent. The conditions for a parallelogram are not met.

• Yes. Opposite angles are congruent to each other. This is sufficient evidence to prove that the quadrilateral is a parallelogram.

• Yes. Opposite sides are congruent to each other. This is sufficient evidence to prove that the quadrilateral is a parallelogram.

• Yes. One set of opposite sides are congruent, and one set of opposite angles are congruent. This is sufficient evidence to prove that the quadrilateral is a parallelogram.

Tags

CCSS.HSG.CO.C.11

If this is a right triangle, find the measure of x to the nearest hundredth.

• 42°

• 41.98°

• 41.99°

• 45°

Tags

CCSS.HSG.SRT.C.8

A wooden frame has screws at A, B, C, and D so that the sides of it can be pressed to change the angles occurring at each vertex. AB ≅ CD and AB ∥ CD, even when the angles change. Why is the frame always a parallelogram?

• The angles always stay the same, so ABCD is a parallelogram.

• All sides are congruent, so ABCD is a parallelogram.

• One pair of opposite sides is congruent and parallel, so ABCD is a parallelogram.

• One pair of opposite sides is congruent, so ABCD is a parallelogram.

Tags

CCSS.HSG.CO.C.11

Prove that circle A with center (-1,1) and radius 1 is similar to circle B with center (-3,2) and radius 2.

• Circle A can be mapped to circle A' by a translation (x,y)→ (x - 2, y + 1). Then circle A' can be mapped to circle B by a dilation with scale factor ½. So, circles A and B are similar.

• Circle A can be mapped to circle A' by a translation (x,y)→ (x + 1, y - 2). Then circle A' can be mapped to circle B by a dilation with scale factor 2. So, circles A and B are similar.

• Circle A can be mapped to circle A' by a translation (x,y)→ (x +1, y - 2). Then circle A' can be mapped to circle B by a dilation with scale factor ½. So, circles A and B are similar.

• Circle A can be mapped to circle A' by a translation (x,y)→ (x- 2,y +1). Then circle A' can be mapped to circle B by a dilation with scale factor 2. So, circles A and B are similar.

Tags

CCSS.8.G.A.4

CCSS.HSG.SRT.A.2

Tags

CCSS.HSG.CO.B.7

Solve the triangle. m∠N = 118°, m∠P = 33°, and m = 15. Round to the nearest tenth.

• m∠M= 29°, n ≈ 27.3, p ≈ 13.4

• m∠M= 29°, n ≈ 8.2, p ≈ 13.4

• m∠M= 29°, n ≈ 27.3, p ≈ 16.9

• m∠M= 29°, n ≈ 8.2, p ≈ 16.9

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Use the given measurements to solve ∆ABC. Round to the nearest tenth.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11