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Analytic Geometry

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Analytic Geometry

EOCT Review

- 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

- Identify the property that justifies the statement.
- m = n, so n = m
- KL = KL
- p = q and q = -1, so p = -1

- Algebraic Proof
- Solve the equation below. Write a justification for each step.
- 1/5(a + 10) = -3

- Properties of Parallelograms
- - Opposite sides are parallel and congruent
- - Opposite angles are congruent
- - Consecutive angles are supplementary
- - Diagonals bisect each other

- WXYZ is a parallelogram.
- Find the measure of angle W.
- Find the value of x.

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

- ABCD is a parallelogram. Find AB and BX.

- In parallelogram DEFG, what is EG?

- Corresponding Angles are congruent
- Alternate Interior Angles are congruent
- Alternate Exterior Angles are congruent
- Same Side Interior Angles are supplementary

- Find each angle measure.

- Find x.

- 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

- If ΔKLM ≅ΔRST, find the value of x.

- What is the measure of angle U?

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

- 3 Triangle Similarity Theorems
- Side-Side-Side
- Side-Angle-Side
- Angle-Angle

- What theorem proves the triangles are similar?

- What theorem proves the triangles are similar?

- What is the length of AC?

- Find SP.

- 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.

- Find measure of <RST.

- Find QR. What type of segment is QR?

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

- 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?

- 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.

- 45-45-90
- Find the value of x.

- 30-60-90
- Find the value of x.

- SOHCAHTOA
- Sin = opp/hyp
- Cos = adj/hyp
- Tan = opp/adj

- 1. Find tan K.
- 2. Find cos M.
- 3. Find sin K.
- 4. To the nearest degree, what is the measure of <M?

- 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?

- 1. Find sin (1.54).
- 2. If sin A = 8/17, find the measure of angle A.

- Use the figure below to find each of the following:
- 1. m<A.
- 2. length of AB
- 3. m<B.

- Use the figure below to find each of the following:
- Chord
- Secant
- Tangent
- Diameter
- Radius

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

- 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.

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

- Opposite angles in an inscribed quadrilateral are supplementary.

- Find the measures of arcs MN and XY.
- Formula is not on the sheet

- Find the areas of sectors BAC and QPR.
- Formula is not on the sheet

- Volume and Surface Area formulas are on the sheet
- Find the volume and surface area of the sphere.

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

- All formulas are on the sheet
- Find the volume of each figure below.

- Find the volume of the cylinder.

- Find the volume of each pyramid.

- Find the volume of the cone.

- Find the volume of the composite figures.