Post Test: Congruence, Proof, and Constructions

Points A(-2, 4), B(1, 3), C(4, -1) and D form a parallelogram. What are the coordinates of D?

(1, 0)

In ΔPQR, , , and are the medians, and and intersect at the point (4, 5). intersects at the point

(4,5)

In parallelogram LMNO, LM = 4.12, MN = 4, LN = 5, and OM = 6.4. Diagonals and intersect at point R. What is the length of ?

3.2

The triangles in the diagram are congruent. If mF = 40°, mA = 80°, and mG = 60°, what is mB?

40°

Match the statements with their values.

55°- m∠ABC when m∠BAC = 70°and ΔABC is an isosceles triangle with AB=AC 180°- m ∠ABC + m∠BAC + m∠ACBwhen ΔABC is an isosceles triangle with AB=AC 45°- m∠BDE when m∠BAC = 45°and points D and E are the midpoints of AB and BC, respectively, in ΔABC 30°- m∠QPR when m∠QRP = 30°and ΔPQR is an isosceles triangle with PQ=QR

Which triangles are congruent according to the SAS criterion?

ABC, FGE, and PQR

bisects at point G. If AE = BE, which equation must be true?

AG = BG

In the figure, transversal t intersects the parallel lines a and b. ∠2 ≅ ∠7 The theorem by which they are congruent is the BLANK

Alternate Exterior Angles Theorem

Study this incomplete image of a geometric construction. This image may result from the construction of BLANK 1. The next step in this construction is to set the compass width to BLANK 2.

BLANK 1- an angle congruent to a given angle BLANK 2- arc JK and draw an arc centered at L intersecting the existing arc through L

The pair of triangles that are congruent by the ASA criterion is BLANK The pair of triangles that are congruent by the SAS criterion is BLANK

BLANK 1- triangle ABC and triangle XYZ BLANK 2- triangle BAC and triangle RQP

What is the missing step in the given proof?

For parallel lines cut by a transversal, corresponding angles are congruent, so ∠OCP ≅ ∠ABC.

You are constructing a copy of . You choose a point, C, as one of the endpoints for the new line segment. What is the next step in the construction?

Keep the compass needle on A, and stretch the compass width to B.

What is the next step in the given proof? Choose the most logical approach.

Statement: CE = DF Reason: Transitive Property of Equality

What needs to be corrected in this construction of a line parallel to AB passing through C?

The second arc should be centered at C.

What is the reason for step 3 of this proof?

Vertical Angles Theorem

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Quadrilateral JKLM has vertices J(8, 4), K(4, 10), L(12, 12), and M(14, 10). Match each quadrilateral, described by its vertices, to the sequence of transformations that will show it is congruent to quadrilateral JKLM.

a translation 2 units right and 3 units down- O(10,1), P(6,7), Q(14,9), and R(16,7) a sequence of reflections across the x- and y-axes, in any order- A(-8, -4), B(-4, -10), C(-12, -12),and D(-14, -10) a translation 3 units left and 2 units up- E(5,6), F(1,12), G(9,14), and H(11,12) a translation 3 units down and 3 units left- W(5,1), X(1,7), Y(9,9), and Z(11,7)

Which construction might this image result from?

construction of a perpendicular to a line through a given external point

What is the reason for statement 3 in this proof?

definition of midpoint

Transversal t cuts parallel lines a and b as shown in the diagram. Which equation is necessarily true?

m∠3 + m∠5 = 180°

In the figure, AC and BD bisect each other. Complete the statements to prove that quadrilateral ABCD is a parallelogram.

m∠AEB = m∠CED =Vertical Angles Theorem BC║AD = converse of Alternate Interior Angles Theorem

If ABC DEC, what is the value of x

x = 1

In the figure, line a and line b are parallel. Based on the figure, match each given angle with its congruent angles.

∠3,∠7,∠6- angles congruent to ∠2 ∠3,∠7,∠2- angles congruent to ∠6 ∠4,∠8,∠5- angles congruent to ∠1 ∠3,∠6,∠2- angles congruent to ∠7

The diagram shows , , and . Which statement can be proven true from the diagram?

∠DGB is supplementary to ∠CGB.