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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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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
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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