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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

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.



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.



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.




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?



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.






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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