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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

Angles formed by Lines and Transversals

- Find each angle measure.

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
- 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.

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.

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