Review Session 1 Practice Problems l. The vertices of … Centroid: 2:1 Ratio For seqments In triangle ABC, AD, CF, and BE are medians. If CF = 33, find CG and FG. c 76) Side-Anqle

Review Session 1 Practice Problemsl. The vertices of AJKL have coordinates J(5,1), K(—2,—3), and Under which transformation is the

image AJ'K tL t not congruent to AJKL?

l) a translation of two units to the right andtwo units down

2) a counterclockwise rotation of 180 degreesaround the origin

3 a reflection over the x-axis4) dilation with a scale factor of 2 and ——9

entered at the origin

2. Triangle ABC and triangle DEF are graphed on the set of axes below.

Which sequence of transformations maps triangle ABC onto triangle DEF?1) reflection over the x-axis followed by a

reflection over the y-axis2) a 1800 rotation about the origin followed by

a reflection over the line y — x

3) a 900 clockwise rotation about the origin

followed by a reflection over the y-axis

4) a translation 8 units to the right and I unit up

followed by a 900 counterclockwise rotation

about the origin

3. Quadrilateral ABCD is graphed on the set of axes below.

When ABCD is rotated 900 in a counterclockwise direction about the

origin, its image is quadrilateral A 'BCD'. Is distance preserved under

this rotation, and which coordinates are correct for the given vertex?

no and C' (l, 2)

no and D (2,4)

yes and A ' (6, 2)

02 and B' (—3, 4) 1 —C c

4. If AA'BC is the image of AABC, under which transformation will the triangles not congruent?

1) reflection over the x-axis

2 translation to the left 5 and down 4

ilation centered at the origin with scale

ctor 2

4) rotation of 2700 counterclockwise about the

origin

5. A sequence of transformations maps rectangle ABCD onto rectangle

A"B"C"D", as shown in the diagram below.

Which sequence of transformations maps ABCD onto A 'B'C'D' and then

s A 'BCD' onto A

I a reflection followed by a rotation

2) a reflection followed by a translation

3) a translation followed by a rotation

4) a translation followed by a reflection

6. In the diagram of parallelogram FRED shown below, ED is extended to A, and AF is drawn such that

If mZR- 1240 , what is mZAFD9

1) 1240

2) 1120

3) 680 i 564) 560

7. In the diagram below, which single transformation was used to map triangle A onto triangle B?

l) line reflection

3) dilation4) translation

8. Which statement is sufficient evidence that ADEF is congruent to AABC?

DE and BC-EF

ZC=ZF3) There is a sequence of rigid motions that

maps AB onto DE, BC onto BF, and AC

onto DF

4 There is a sequence of rigid motions that

C

maps point A onto point D, B onto DE, andzB ontoZE, ?

. Triangle ABC is graphed on the set of axes below. Graph and label AA 'B' C', the image of AABC after a

reflection over the line x = 1.

x

10. As graphed on the set of axes below, AA t B' C' is the image of AABC after a sequence of transformations.

x

11. In parallelogranHBCD shown below, diagonals AC and BD intersect at E.

c

Prove: ZACD. ZCABStatements Reasons

l. tn parallelogram ABCD shown below, diagonals 1. Given

3' ah(S)

Guided Practice

Riqht Trianqles:

12. To find the sides of a right triangle use the Pythagorean Theorem.

2 2 (Remember that the a and b make up right angle)

23

11

x

simpl$ð

2

13) Theorem: The measure of an exterior angle of a triangle is

equal to the sum of the measures of the two remote interior

angles of the triangle. d + c— ISO

In the diagram below of AIIQP, side is extended through P to T, rnLQPT = 6.r + 20,

mt.-HQP = x + 40, and mZPHQ = 4x —5. Find mLQPT.

(6x + 20)0

p

(Not drawn to scale)

14) Isosceles Triangles:

IS

1100

The base angles of an isosceles triangle are equal in measure.

The sides opposite the base angles in an isosceles triangle (called legs) are equal in length.

Given the following find the degrees in each angle ofthe triangle.

OCA =c

50

60X SO

15) Centroid: 2:1 Ratio For seqmentsIn triangle ABC, AD, CF, and BE are medians. If CF = 33, find CG and FG.

c

76) Side-Anqle Relationship

The longest side is across From the largest angle•

The medium length side is across From the medium-sized angle•

The shortest side is across From the smallest a 9 e

In triangle DOG, 111<1) = 40, m<0 60, and m<G = 80.

State the longest side of the triangle

• State the shortest side of the triangle

17. In the accompanying diagram,HK bisects IL and ZHE LK.

Prove: HI KL

Statements

1. HK bisects IL and

2,

5 z I-JF-

Reasons

1. Given

h Vs

s, cpcÇC

18) Given:Äb Il

AACB

Prove: S

G.

L

c

19) Graph and state the coordinates of AA'B'C', the image of AABC with A(1,2), B(3,O) and C(6,8)after thecomposition T2,oo R1800.

20. Graph triangle ABC. A(l, 1), B(4, 5), C(3, 2) and reflect it through point (-2, 1). Label your image.

Bi(-m-3)

C' 010)

Use rigid motions to explain why the pre-image and image are congruent.

pŸtSRJVR

21. In the diagram of trapezoid ABCD below, diagonals ACand BDintersect at E and A ABC ¥ ADCB.

Which statement is true based on the given information? C

1) ACE BC 3) ZCDE= CAD2) CD-AD 4) ZCDB= ZBAC

cpcTc D