Analytic Geometry

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# Analytic Geometry - PowerPoint PPT Presentation

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&lt;1 + m&lt; 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

EOCT Review

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

Proofs
• Identify the property that justifies the statement.
• m = n, so n = m
• KL = KL
• 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
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.
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
• 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?
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
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
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.
• 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.