[PDF] Study Guide and Intervention PDF Geometry%20Study%20Guide.pdf

1 jui 2014 · lnterior Angle I lf a convex polygon has n sides, and S is the sum of the measures of its interior angles, SumTheorem I then S= 180(n - 2) A

Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle In ⨀G, minor arc ̂ is the

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_PERIOD NAME DATE - 10-4 Study Guide and Intervention Inscribed Angles Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and

[PDF] Study Guide and Intervention Inscribed Angles

Study Guide and Intervention Inscribed Angles An inscribed angle is an angle whose vertex If an angle is inscribed in a circle, then the measure of the

[PDF] 9-4 Study Guide and Intervention

Glencoe Geometry 9-4 Study Guide and Intervention Inscribed Angles Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose

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Lesson 10-1 10-1 Study Guide and Intervention (continued) Find m DEF DEF is an inscribed angle so its measure is half of the intercepted arc m DEF 1 2

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Example Exercises Lesson 10-4 Chapter 10 27 Glencoe Geometry 10-4 Study Guide and Intervention Inscribed Angles NAME

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10-4 Study Guide and Intervention Inscribed Angles Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords

[PDF] Study Guide and Intervention Workbook - Metrolina Regional

5 déc 2018 · completed Study Guide and Intervention Workbook can help you in reviewing for 3-2 Angles and Parallel Lines 10-4 Inscribed Angles

[PDF] Study Guide and Intervention

1 jui 2014 · lnterior Angle I lf a convex polygon has n sides, and S is the sum of the measures of its interior angles, SumTheorem I then S= 180(n - 2) A

DATE PERIOD

-Study Guide and Intervention

Angles of Polygong

Sum of Measures of lnterior Angles The segments that connect the nonconsecutive sides of a polygon are called diagonals. Drawing all of the diagonals from one vertex of an z-gon separates the polygon into n - 2 triangles. The sum of the measures of the interior angles of the polygon can be found by adding the measures of the interior angles of those n - 2triangles.

lnterior Angle I lf a convex polygon has n sides, and S is the sum of the measures of its interior angles,

SumTheorem I then S= 180(n - 2).

A convex polygon hasffi Tbemeasureofan

18 sides. Find the sun of the measuresinterior angle of aregular polygon is

120. Find the number of sides.

The number of sides is z, so the sum of the

measures of the interior angles is 1202.S: 190(n _ Z)

12An: 180(z - 2)

12On=1802-360

-60n : -360n=6 ffif{?frtrx Find the sum of the measures of the interior angles of each corlvex polygon. of the interior angles.S=180(z-2) = 180(13 - 2):190(11): 1980

1. 10-gon

4.8-gon

7. 150

10.165 13. Find r.

2.16-gon

5. 12-gon

8.160

11. 168.?5

3.30-gon

6.3r-gon

Ihe measure of nn interior angle of a regular polygon is given. Find the number of sides in each polygon.

9. 175

12. 135

(6x+ 10)"

4'.17Glencoe Geometry

DATE PERIOD

-Study Guide and Intervention

Parallelograms

Sides and Angles of Parallelograms A quadrilateral with both pairs of opposite sides parallel is a parallelogram. Here are four important properties of parallelograms.

P-a//s+4

lf POFS is a parallelogram, then

The opposite sides of a

parallelogram are cugruent.ffi=SRandF3=OR

The opposite angles of a

parallelogram are congruent.zP= zRand LS= LQ

The consecutive angles of a

parallelogram are supplementary. tPand LSare supplementary; zSand zRare supplementary; eFland t-Qxa supplementary; z-Qarfr LPare supptementary. lf a parallelogram has one right angle, then it has four right angles.

It mLP: 90, then mLQ: 90, mtR: 90, and mtS = 9t).

ffi ffABcDis a parallelogra*, find o and b.

2a: 34a:17

/A and LC arc opposite angles, so tA = LC.

8b = LLZ

b=L4 ffiiluprn

Find r and y in each parallelogram.

t.8yt-6FlLI 8B /a* p,e/ 2.

2yso,[-ltso

72x
4. 6."ff o GlencoelMcGraw-Hill423Glencoa Gaometry

DATE PERIOD

-Study Guide and Intervention

Rectangles

Properties of Rectangles A rectangle is a quadrilateral with fourright angles. Here are the properties of rectangles.

A rectangle has all the properties of a parallelogram.. Opposite sides are parallel.. Opposite angles are congfuent.. Opposite sides are congruent.r Consecutive angles are supplementary.r The diagonals biseet each other.

Also:. All four angles are right angles. LUTSJTSR, LSRU, antd, /RUT are right angles.r The diagonals are congruent. TR = l1g

tffiffi In rectangle RsTa above, US = 6f, + S and Bf = 7x - 2.Findr.

The diagonals ofa rectaagle biseet each

other, so US = RT.

6s+3=7x-Z3:x*2

5=tc flHatHfrn ffi rnrectangleuilTU above, wLSTR = 8r * S and wLUTR =16r - 9. Find wLSTR.

LUTS is a right angle, sowLSTR * wLUTR :90.

&+3+16x-9:9024xt-6:90

24x = 96x=4

mLsTR: gr + 3: g(4) + 3or35

ABCD is a reetangle. B

l.lfAE = 36 and CE = 2x - 4,findr.

2.If BE:6y + 2 and CE:4y * 6,findy. A

S.If BC = 24 andAD: 5y - 1, findy.

4.Tf wLBEA: 62, find wLBAC.

5.If m/AED = LZx and rn.LBEC = L0x + 20, find mtAED.

6.1{ BD = 8y - 4 and AC = 7y * 3,frndBD.

l.If ruLDBC : 10r and.rn/ACB : fo;z- 6, find rnLACB.

8. IfAB : 6y and BC :8y, find BD in terms ofy.

9. In rectangLe MNAP,wLL = 40. Find the measure of each

numbered angle. o GlencoeAlcGraw-Hill435Glencoe Geometry

DATE PERIOD

-Study Guide and Intervention

Rhombt and Squares

PropertieS of Rhombi e rhombus is a quadrilateral with four congruent sides. Opposite sides are congruent, so a rhombus is also a parallelogram and has all of the properties of a parallelogram. Rhombi also have the following properties.

The diagonals are perpendicular.Mfr lHD

Each diagonat bisects a pair of opposite angles.Mff bisects IRMO and LRHO. ffinisects IMRHand LMOH. ll the diagonals of a parallelogram are perpendicular, then the figure is a rhombus. ll RHOMiS a parallelogram and RO L MH, lhen RHOM is a rhombus. ffi rnrhombusABCD,mSAC = B2.Findthe measure of each numbered angle. ABCD is a rhombus, so the diagonals are perpendicular and LABE A is a right triangle. Thus rzZ4 = 90 and m.Lt:90 - 32 or 58. The diagonals in a rhombus bisect the vertex angles, so mLL = mLZ.

Thus, mLZ:58.

A rhombus is a parallelogram, so the opposite sides are parallel. IBAC aud l-3 are alternate interior angles for parallel lines, so n'tll = *2. ffiilffi

ABCD is a rhombus.

L.If m/ABD = 60, find m.LBDC.

S. IfAB = 26 and BD :20, findAE.

6.If m,LCBD = 58, find m/ACB.

Z.If AE = 8, findAC.

4. Find rnLCEB. A

6.Tf AE : 3.r - 1 and AC : 16, find r.

7.If nTLCDB = 6y and m/ACB :2y + 10, findy.

8. IfA"D = ?at + 4 and CD = 4n * 4, find x.

9. a. What is the midpoint ofE-nZ

b. What is the midpoint ot CJ? c. What kind of figure is FGHJ? Explain. d. What is the slope ofF?/? e. What is the slope of GJ? f. Based on parts c, d, and e, what kind of {igure is FGIIJ?

441o Glencoe/McGraw-Hill

Explain.

Glencoe Geometry

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-Study Guide and Intervention ftontinued)

Trapezoids

Medians of Trapezoids The median of a trapezoid is the segment that joins the midpoints of the legs. It is parallel to the bases, and its length is one-half the sum of the lengths of the bases.

In trapezoi d, HJI{L, MN : }W"t + LK).

ffi ffi is the median of trapezoid BsrU. Find r. MN= 80=
30=

30=5=r

ffiilffi RS

H3x+5S

+ UT) -5*9xr* ?e.\ 3x L2 ft L(2' fr 6xc _b) MN is the median of trapezoid H,IKL. Fiad each indicated value. A---------:!

1. Find MN itHJ= 82 and LK: Go. Uaq

2. Find LKif HJ = 18 and MN : 28.

8. Find MN if HJ + LK: 42.

4. Find wLLMN tf rntLHJ = 116.

5. Find wLJKL it HJKL is isoseeles and wLHLK : 62.

6. Find HJ itMN: 5* + 6,HJ = 3* + 6, and LK - 8x.

7. Find the length of the median of a trapezoid with verticesA(2,2), B(3, 3), C(7,0), and D{8, -2).

o Glencoe/McGrawHillM8Glencae Geometry

Study Guide and Intervention

Circles and Circumterence

Pafts of Circlgs A circle consists of all points in a plane that are agiven distance, called the radius, from a given point called the center.

A segment or line can interseet a circle in several ways.r A segment with endpoints that are the center of the eircle and

a point of the circle is a radius.. A segment with endpoints that lie on the circle is a chord.. A chord that contains the circle's center is a diameter.

a" Name the circle.

The name of the circle is OO.

b. Name radii of the circle. m, Bo,co, and DD are radii. c. Name chords of the circle.

A.B and ffi are chords.

d. Name a diameter of the circle.

AA ir a diameter.

ffiffiffin

DATE PERIOD

A,a7-',, -eV )P4)

choro:rl ED rat ius: E, E, E diameter: E

1. Name the circle.

2. Name radii of the circle.

S. Name chords of the circle.

4. Name diameters of the circle.

5. FindAA ifAB is 18 millimeters.

6. Find "4.r8 and AB if -BY is 1^0 inches.

7.IsA.B =ffit Explain.

541o GlencoelMcGraw-HillGlencoe Geometry

PERIOD

6F is a rninor arc.ffi is a major are.

LGEFiS a central angle.

nLHEC+ mLCEF+ mLFEG+ mLGEH:3ffi ni6F - nzCEF n;edF-s6o-mOF nieF+niFG=m€A {ffiffi rn oft, tnARB = 42 andl? is a diarneten

Fiudarffi sllldmffi.

/ARB is a central angle and, rruIARB = 42, sa nr@ = 42.

Thus nffi = 360 * 42 or 318.

ffiAHilM

Study Guide and Intervention

Angles and Arcs

Angles and ArCs A central angle is an angle

whose vertex is at the center of a circle and whose sides are radii. A central angle separates a circle into tvro arcs, a mqior arc and a minor arc.

Here are some properbies of central angles and arcs.r The sum of the measures of the eentral angles of

a cirele with no interior points in common is 360,. The measure of a minor arc equals the measure of its central angle.r The measure of a major arc is $60 minus the measure of the minor are.r T\vo arcs are congruent if and only if their corresponding eentral angles are congruent.. The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.(Arc Addifion Fostulate)

Find each measure.

1. wLSCT

8. ruLSCQ

7, mCD

s. nficD

2, mzSCU

4. wLQCT

T@ lf m/3OA = d,$,, frnd eaeh measune.

6. rnEE 6. lrfid

8. nACB

10.ntfr

o Glencoe/McGraw-Hill547Glencoe Geometry

DATE PEHIOD

-Study Guide and Intervention pontinued)

Angles and Arcs

Afc Length An arc is part of a circle and its length is a part of the circumference of the circle.

ffi hro*, ,L4,,B- 1BE, RB -8randffi is a diameten Find the length atffi.m/ARB: 135, so *ffi = 135. Using the formula C : Zrr,the

ctrcumference is 2n(8) or 16r. To find the length offfi', write a proportion to compare eaeh part to its whole. tensthjfffi : degrryqeasuregf 3rg_ proportioncircumference degree measure of circle( _13516n' 360 " (16nX135)I:-" 360 = 6tt Simplify.

The length ofG is 6zr or about 18.85 units.

ffiffi $ubstitution

Multiply each side by 1&r.

the diameter of @ is 24 units long. Find the leugth of eaeh are for the given angle rneaslrrer t.6E if maog: 120 z.frm. if mLDoE * LZo

S. FD tf ruLCOB = 45

*eEi. if mlcoB : 45

T'lre diarneter of OP is l5 units Iong and LSPT a LnPf.Find the length of each are for the given angle meaflre.

6.m if ruLSW : 7o

6. Im tf ruLRW : 5A

7, MST

8.I{ES tf ruLMPS : 140

"ffi, e Glencoe/Mccraw-Hill548Glencae Geomeuy

DATE PEHIOD

-Study Guide and Intervention ftontinued)

Arcs and Chords

Diameters and Chordsr In a circle, if a diameter is perpendicular to a chord, then it bisects the chord andits arc.o In a circle or in congruent circles, two chords are congruent ifand only ifthey are equidistant from the center.Z tW t44,then 7X = ffi anafu ='frd. ll OX= OY,thenIE=E tt XE = ffi then 7E and ffi are equidistant from point O. ffi rn oo, 6 tffi,oo= 18, and cD = z/..Findr. A diameter or radius perpendicular to a ehord bisects the chord, so,8D is half of CD.

1ED :;(24)

=L2

Use the P;rthagorean Theorem to find x tn LOED.

(ODz + (ED)z = (OD)Z Pythasorean rheorem x2 + L22 = L52 substitutionx2+144=22512: 81r:9 ffi

[PDF] [PDF] Study Guide and Intervention

DATE PERIOD

Angles of Polygong

SumTheorem I then S= 180(n - 2).

A convex polygon hasffi Tbemeasureofan

18 sides. Find the sun of the measuresinterior angle of aregular polygon is

120. Find the number of sides.

The number of sides is z, so the sum of the

12An: 180(z - 2)

12On=1802-360

1. 10-gon

4.8-gon

7. 150

10.165

13. Find r.

2.16-gon

5. 12-gon

11. 168.?5

3.30-gon

6.3r-gon

9. 175

12. 135

4'.17Glencoe Geometry

DATE PERIOD

Parallelograms

P-a//s+4

The opposite sides of a

The opposite angles of a

The consecutive angles of a

It mLP: 90, then mLQ: 90, mtR: 90, and mtS = 9t).

2a: 34a:17

8b = LLZ

Find r and y in each parallelogram.

2yso,[-ltso

DATE PERIOD

Rectangles

The diagonals ofa rectaagle biseet each

6s+3=7x-Z3:x*2

LUTS is a right angle, sowLSTR * wLUTR :90.

24x = 96x=4

ABCD is a reetangle. B

2.If BE:6y + 2 and CE:4y * 6,findy. A

S.If BC = 24 andAD: 5y - 1, findy.

4.Tf wLBEA: 62, find wLBAC.

5.If m/AED = LZx and rn.LBEC = L0x + 20, find mtAED.

6.1{ BD = 8y - 4 and AC = 7y * 3,frndBD.

8. IfAB : 6y and BC :8y, find BD in terms ofy.

9. In rectangLe MNAP,wLL = 40. Find the measure of each

DATE PERIOD

Rhombt and Squares

The diagonals are perpendicular.Mfr lHD

Thus, mLZ:58.

ABCD is a rhombus.

L.If m/ABD = 60, find m.LBDC.

S. IfAB = 26 and BD :20, findAE.

6.If m,LCBD = 58, find m/ACB.

Z.If AE = 8, findAC.

4. Find rnLCEB. A

6.Tf AE : 3.r - 1 and AC : 16, find r.

7.If nTLCDB = 6y and m/ACB :2y + 10, findy.

8. IfA"D = ?at + 4 and CD = 4n * 4, find x.

9. a. What is the midpoint ofE-nZ

441o Glencoe/McGraw-Hill

Explain.

Glencoe Geometry

DATE PERIOD

Trapezoids

In trapezoi d, HJI{L, MN : }W"t + LK).

30=5=r

H3x+5S

1. Find MN itHJ= 82 and LK: Go. Uaq

2. Find LKif HJ = 18 and MN : 28.

8. Find MN if HJ + LK: 42.

4. Find wLLMN tf rntLHJ = 116.

5. Find wLJKL it HJKL is isoseeles and wLHLK : 62.

6. Find HJ itMN: 5* + 6,HJ = 3* + 6, and LK - 8x.

7. Find the length of the median of a trapezoid with verticesA(*2,2), B(3, 3), C(7,0), and D{*8, -2).

Study Guide and Intervention

Circles and Circumterence

The name of the circle is OO.

7. Find the length of the median of a trapezoid with verticesA(2,2), B(3, 3), C(7,0), and D{8, -2).