Geometry Midterm Low Level

Tina wants to sew a piece of fabric into a scarf in the shape of an isosceles triangle, as shown in the accompanying diagram.

What are the values of x and y?

• x = 42 and y = 96

• x = 69 and y = 69

• x = 90 and y = 48

• x = 96 and y = 42

Which illustration shows the correct construction of an angle bisector?

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Which geometric principle is used to justify the construction?

• A line perpendicular to one of two parallel lines is perpendicular to the other.

• Two lines are perpendicular if they intersect to form congruent adjacent angles.

• When two lines are intersected by a transversal and alternate interior angles are congruent, the lines are parallel.

• When two lines are intersected by a transversal and the corresponding angles are congruent, the lines are parallel.

In △ABC, m∠A = 3x + 1, m∠B = 4x - 17, and m∠C = 5x - 20. Which type of triangle is △ABC?

• Right

• Scalene

• Isosceles

• Equilateral

Natalie is playing with the pinwheel like the one shown in the picture above. Which degree of rotation would carry the pinwheel onto itself?

• 5°

• 125°

• 216°

• 225°

What is the measure of angle b?

• 36^o

• 56^o

• 63^o

• 117^o

If ABCD is a parallelogram, which statement would prove a that ABCD is a rectangle?

• ∠ABC ≅ ∠CDA

• AC ≅ BD

• AC ⟂ BD

• ∠ABD ≅ ∠DBC

As shown in the diagram below, CD is a median of △ABC.

Which statement is always true?

• AD ≅ DB

• AC ≅ AD

• ∠ACD ≅ ∠CDB

• ∠BCD ≅ ∠ACD

Which transformation does not produce an image that is congruent to the original?

• A dilation of scale factor 1 centered at (2,4)

• A dilation of scale factor ½ centered at the origin

• A reflection over y = 4x

• A rotation of 270 degrees followed by a translation down 2

Given: △ABD, BC is the perpendicular bisector of AD Which statement cannot always be proven?

• AC ≅ DC

• BC ≅ CD

• ∠ACB ≅ ∠DCB

• △ABC ≅ △DBC