Post Test: Congruence, Proof, and Constructions

In the figure, CD = EF and AB = CE. Complete the statements to prove that AB = DF. CD + DE = EF + DE by the BLANK 1 Property of Equality. CE = CD + DE and DF = EF + DE by BLANK 2. CE = DF by the BLANK 3 Property of Equality. Given, AB = CE and CE = DF implies AB = DF by the BLANK 4 Property of Equality.

BLANK 1 Addition BLANK 2 IS NOT transitive BLANK 3 Transitive BLANK 4 Transitive

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

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

(1, 0)

Which pair or pairs of polygons are congruent?

1, 2, 3, and 4

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

3.2

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

40°

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

AG=BG

Match the statements with their values. 55° BLANK 1 180° BLANK 2 45° BLANK 3 30° BLANK 4

BLANK 1 m∠ABC when m∠BAC = 70°and ΔABC is an isosceles triangle with AB=AC BLANK 2 m ∠ABC + m∠BAC + m∠ACBwhen ΔABC is an isosceles triangle with AB=AC BLANK 3 m∠BDE when m∠BAC = 45°and points D and E are the midpoints of AB and BC, respectively, in ΔABC BLANK 4 m∠QPR when m∠QRP = 30°and ΔPQR is an isosceles triangle with PQ=QR

The pair of triangles that are congruent by the ASA criterion is BLANK 1 The pair of triangles that are congruent by the SAS criterion is BLANK 2

BLANK 1 triangle ABC and triangle XYZ BLANK2 triangle BAC and triangle RQP

In the figure, A⁢C¯ and B⁢D¯ bisect each other. The length of A⁢B¯ is 12 centimeters and the length of B⁢C¯ is 11 centimeters. The length of A⁢D¯ is BLANK 1 centimeters and the length of D⁢C¯ is BLANK 2 centimeters

BLANK 1- 11 BLANK 2- 12

The sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is a BLANK 1 followed by a BLANK 2

BLANK 1- 90-degree counterclockwise rotation BLANK 2- reflection across the y-axis and a translation 20 units down

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- BLANK 1 ∠3,∠7,∠2- BLANK 2 ∠4,∠8,∠5- BLANK 3 ∠3,∠6,∠2- BLANK 4

BLANK 1- angles congruent to 2 BLANK 2 angles congruent to 6 BLANK 3 angles congruent to 1 BLANK 4 angles congruent to 7

In ΔPQR, P⁢S¯, Q⁢T¯, and R⁢U¯ are the medians, and P⁢S¯ and Q⁢T¯ intersect at the point (4, 5). R⁢U¯ intersects P⁢S¯ at the point BLANK

BLANK- (4,5)

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

BLANK- Alternate Exterior Angles Theorem

What is the missing step in the given proof?

INCORRECT For parallel lines cut by a transversal, corresponding angles are congruent, so ∠ACB ≅ ∠PCQ.

You are constructing a copy of A⁢B¯ . 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 = DFReason: Transitive Property of Equality

What is step 10 in this proof?

Statement: Point P lies on line C'D'.Reason: The coordinates of P satisfy the equation of line C'D'.

What needs to be corrected in this construction of a line parallel to line 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

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 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 2 units right and 3 units down- O(10,1), P(6,7), Q(14,9), and R(16,7) a translation 3 units down and 3 units left- W(5,1), X(1,7), Y(9,9), and Z(11,7) a translation 3 units left and 2 units up- E(5,6), F(1,12), G(9,14), and H(11,12)

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°

Which of these shapes is congruent to the given shape?

the skinny long parallelogram going the opposite way

If ABC DEC, what is the value of x?

x = 1

Which triangles are congruent according to the SAS criterion?

Δ ABC, Δ FGE, and Δ PQR

The diagram shows A⁢B⟷, C⁢D⟷, and G⁢E⟶. Which statement can be proven true from the diagram?

∠DGB is supplementary to ∠CGB.