Transcript Analytic Geometry - Effingham County Schools

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.
1. m = n, so n = m
2. KL = KL
3. p = q and q = -1, so p = -1
Proofs
• Algebraic Proof
• Solve the equation below. Write a justification for each
step.
• 1/5(a + 10) = -3
Parallelograms
• Properties of Parallelograms
• - Opposite sides are parallel and congruent
• - Opposite angles are congruent
• - Consecutive angles are supplementary
• - Diagonals bisect each other
Parallelograms
• WXYZ is a parallelogram.
• Find the measure of angle W.
• Find the value of x.
Parallelograms
• In parallelogram JKLM, what is the value of <K?
Parallelograms
• ABCD is a parallelogram. Find AB and BX.
Parallelograms
• In parallelogram DEFG, what is EG?
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 Transversals
• Find each angle measure.
Angles formed by Lines and Transversals
• Find x.
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
Congruence
• If ΔKLM ≅ ΔRST, find the value of x.
Congruence
• What is the measure of angle U?
Congruence
• ΔJKL≅ ΔMNP. KL = 21x - 2, NP = 20x, LJ = 15x and PM =
13x + 4. Find LJ.
Congruence
Similarity
• 3 Triangle Similarity Theorems
• Side-Side-Side
• Side-Angle-Side
• Angle-Angle
Similarity
• What theorem proves the triangles are similar?
Similarity
• What theorem proves the triangles are similar?
Similarity
• What is the length of AC?
Similarity
• Find SP.
Similarity
Similarity
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
• Find measure of <RST.
Midsegment Theorem
• Find QR. What type of segment is QR?
Midsegment Theorem
Triangles
• What is the length of the longest side of the triangle?
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
• 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 Triangles
• 45-45-90
• Find the value of x.
Special Right Triangles
• 30-60-90
• Find the value of x.
Trigonometry
• SOHCAHTOA
• Sin = opp/hyp
• Cos = adj/hyp
• Tan = opp/adj
Trigonometry
• 1. Find tan K.
• 2. Find cos M.
• 3. Find sin K.
• 4. To the nearest degree, what is the measure of <M?
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?
Trigonometry
• 1. Find sin (1.54).
• 2. If sin A = 8/17, find the measure of angle A.
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
• Use the figure below to find each of the following:
• Chord
• Secant
• Tangent
• Diameter
• Radius
Lines that Intersect Circles
• To the nearest tenth, what is the length of MN?
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 Angles
• Find the measure of arc JK. Then, find the measure of
arc JIL.
Central and Inscribed Angles
Central and Inscribed Angles
Central and Inscribed Angles
Central and Inscribed Angles
Inscribed Quadrilaterals
• Opposite angles in an inscribed quadrilateral are
supplementary.
Arc Length
• Find the measures of arcs MN and XY.
• Formula is not on the sheet
Sector Area
• Find the areas of sectors BAC and QPR.
• Formula is not on the sheet
Spheres
• Volume and Surface Area formulas are on the sheet
• Find the volume and surface area of the sphere.
Spheres
• Find the surface area of a sphere with a volume of 256Π
cm3
Volume
• All formulas are on the sheet
• Find the volume of each figure below.
Volume
• Find the volume of the cylinder.
Volume
• Find the volume of each pyramid.
Volume
• Find the volume of the cone.
Volume
• Find the volume of the composite figures.