Analytic geometry
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Analytic Geometry. EOCT Review. Proofs. Which item can be given as a statement in a proof? A. Given B. Def. of congruent segments C. m<1 + m< 2= 180 D. Trans. Prop. of Equality. Proofs. Identify the property that justifies the statement. m = n, so n = m KL = KL

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Analytic Geometry

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Analytic geometry

Analytic Geometry

EOCT Review


Proofs

Proofs

  • Which item can be given as a statement in a proof?

  • A. GivenB. Def. of congruent segmentsC. m<1 + m< 2= 180

    D. Trans. Prop. of Equality


Proofs1

Proofs

  • Identify the property that justifies the statement.

  • m = n, so n = m

  • KL = KL

  • p = q and q = -1, so p = -1


Proofs2

Proofs

  • Algebraic Proof

  • Solve the equation below. Write a justification for each step.

  • 1/5(a + 10) = -3


Parallelograms

Parallelograms

  • Properties of Parallelograms

  • - Opposite sides are parallel and congruent

  • - Opposite angles are congruent

  • - Consecutive angles are supplementary

  • - Diagonals bisect each other


Parallelograms1

Parallelograms

  • WXYZ is a parallelogram.

  • Find the measure of angle W.

  • Find the value of x.


Parallelograms2

Parallelograms

  • In parallelogram JKLM, what is the value of <K?


Parallelograms3

Parallelograms

  • ABCD is a parallelogram. Find AB and BX.


Parallelograms4

Parallelograms

  • In parallelogram DEFG, what is EG?


Angles formed by lines and transversals

Angles formed by Lines and Transversals

  • Corresponding Angles are congruent

  • Alternate Interior Angles are congruent

  • Alternate Exterior Angles are congruent

  • Same Side Interior Angles are supplementary


Angles formed by lines and transversals1

Angles formed by Lines and Transversals

  • Find each angle measure.


Angles formed by lines and transversals2

Angles formed by Lines and Transversals

  • Find x.


Congruence

Congruence

  • 5 Triangle Congruence Theorems

  • Side-Side-Side

  • Side-Angle-Side

  • Angle-Angle-Side

  • Angle-Side-Angle

  • Hypotenuse Leg (right triangles only)

  • Angle-Side-Side is NOT a theorem


Congruence1

Congruence

  • If ΔKLM ≅ΔRST, find the value of x.


Congruence2

Congruence

  • What is the measure of angle U?


Congruence3

Congruence

  • ΔJKL≅ΔMNP. KL = 21x - 2, NP = 20x, LJ = 15x and PM = 13x + 4. Find LJ.


Congruence4

Congruence


Similarity

Similarity

  • 3 Triangle Similarity Theorems

  • Side-Side-Side

  • Side-Angle-Side

  • Angle-Angle


Similarity1

Similarity

  • What theorem proves the triangles are similar?


Similarity2

Similarity

  • What theorem proves the triangles are similar?


Similarity3

Similarity

  • What is the length of AC?


Similarity4

Similarity

  • Find SP.


Similarity5

Similarity


Similarity6

Similarity


Similarity7

Similarity

  • A drawing of a garden uses a scale of 1 in : 3 ft. Find the length of the garden if the length on the drawing is 13 inches.


Exterior angles theorem

Exterior Angles Theorem

  • Find measure of <RST.


Midsegment theorem

Midsegment Theorem

  • Find QR. What type of segment is QR?


Midsegment theorem1

Midsegment Theorem


Triangles

Triangles

  • What is the length of the longest side of the triangle?


Angle relationships in triangles

Angle relationships in Triangles

  • What is the value of x if the acute angles of a right triangle measure 8x° and 12x°?

  • The angles of a triangle measure 4°, 86°, and 90°. Which classification of the triangle is correct?

  • One angle of an equilateral triangle measures (4x - 20). What is the value of x?


Special right triangles

Special Right Triangles

  • There are 2 types of special right triangles:

  • 1. 45-45-90

  • In a 45-45-90 triangle, the legs have equal length and the hypotenuse is the length of one of the legs multiplied by √2.

  • 2. 30-60-90

  • In a 30-60-90 triangle, the hypotenuse is the length of the shorter leg multiplied by 2, and the longer leg is the length of the shorter leg multiplied by √3.


Special right triangles1

Special Right Triangles

  • 45-45-90

  • Find the value of x.


Special right triangles2

Special Right Triangles

  • 30-60-90

  • Find the value of x.


Trigonometry

Trigonometry

  • SOHCAHTOA

  • Sin = opp/hyp

  • Cos = adj/hyp

  • Tan = opp/adj


Trigonometry1

Trigonometry

  • 1. Find tan K.

  • 2. Find cos M.

  • 3. Find sin K.

  • 4. To the nearest degree, what is the measure of <M?


Trigonometry2

Trigonometry

  • A 24-foot ladder forms a 76° angle with the ground. The top of the ladder rests against a building. To the nearest inch, how high up the building does the ladder reach?

  • One acute angle of a right triangle measures 28°. To the nearest tenth, what is the length of the side opposite that angle if the hypotenuse measures 16 meters?

  • A skateboard ramp makes a 22° angle with the ground. To the nearest foot, how high is the ramp?


Trigonometry3

Trigonometry

  • 1. Find sin (1.54).

  • 2. If sin A = 8/17, find the measure of angle A.


Trigonometry4

Trigonometry

  • Use the figure below to find each of the following:

  • 1. m<A.

  • 2. length of AB

  • 3. m<B.


Lines that intersect circles

Lines that Intersect Circles

  • Use the figure below to find each of the following:

  • Chord

  • Secant

  • Tangent

  • Diameter

  • Radius


Lines that intersect circles1

Lines that Intersect Circles

  • To the nearest tenth, what is the length of MN?


Central and inscribed angles

Central and Inscribed Angles

  • A central angle is EQUAL to the measure of its intercepted arc.

  • An inscribed angle is HALF the measure of its intercepted arc.

  • An angle inscribed in a semicircle is ALWAYS a right angle.

  • If two inscribed angles intercept the same arc, the angles are congruent.


Central and inscribed angles1

Central and Inscribed Angles

  • Find the measure of arc JK. Then, find the measure of arc JIL.


Central and inscribed angles2

Central and Inscribed Angles


Central and inscribed angles3

Central and Inscribed Angles


Central and inscribed angles4

Central and Inscribed Angles


Central and inscribed angles5

Central and Inscribed Angles


Inscribed quadrilaterals

Inscribed Quadrilaterals

  • Opposite angles in an inscribed quadrilateral are supplementary.


Arc length

Arc Length

  • Find the measures of arcs MN and XY.

  • Formula is not on the sheet


Sector area

Sector Area

  • Find the areas of sectors BAC and QPR.

  • Formula is not on the sheet


Spheres

Spheres

  • Volume and Surface Area formulas are on the sheet

  • Find the volume and surface area of the sphere.


Spheres1

Spheres

  • Find the surface area of a sphere with a volume of 256Π cm3


Volume

Volume

  • All formulas are on the sheet

  • Find the volume of each figure below.


Volume1

Volume

  • Find the volume of the cylinder.


Volume2

Volume

  • Find the volume of each pyramid.


Volume3

Volume

  • Find the volume of the cone.


Volume4

Volume

  • Find the volume of the composite figures.


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