Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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day 4 - thursday, september 11th fill in the missing statements in the …
4. Substitution property of equality
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if both dimensions are doubled, then which of the following will be tru…
The new perimeter will be 2 times the old perimeter.
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day 3 - wednesday, september 10th true or false: if two angles are supp…
True
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if the side lengths are doubled, then which of the following statements…
The new area will be 4 times the old area.
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symmetry: x - axis y - axis origin none of these graph 1 symmetry: x - …
Graph 1: none of these Graph 2: x - axis, y - axis, origin Graph 3: y - axis
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look at this square: if the side lengths are tripled, then which of the…
The new perimeter will be 3 times the old perimeter.
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if the side lengths are tripled, then which of the following will be tr…
The new perimeter will be 3 times the old perimeter.
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look at this square: 8 m 8 m if the side lengths are doubled, then whic…
The new perimeter will be 2 times the old perimeter.
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quick proof sketch: if ∠p and ∠q are right angles, and ∠p and ∠r are su…
$\angle Q\cong\angle R$ is proved by showing $m\angle Q=m\angle R = 90^{\circ}$ through the properties of right - angles and supplementary angles.
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question 1 of 33 which of the following best describes a point of symme…
C. The point about which an image is rotated in rotational symmetry
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triangle l is a scaled copy of triangle k. what is the value of j?
\(65\)
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if ∠x + ∠z = 90° and ∠y + ∠z = 90°, what can you conclude about ∠x and …
∠X = ∠Y
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parallelogram y is a scaled copy of parallelogram x. what is the value …
\(105\)
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polygon k is a scaled copy of polygon j. what scale factor takes polygo…
1.5
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polygon d is a scaled copy of polygon c. polygon c has side - lengths 4…
$\frac{5}{8}$
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day 4 - thursday, september 11th if ∠x + ∠z = 90° and ∠y + ∠z = 90°, wh…
For the first problem: $\angle X=\angle Y$. For the second problem: Outline of steps: 1. Note $\angle P=\angle Q = 90^{\circ}$ as they are right - angles. 2. Use the fact that $\a…
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the minute hand of a clock is 9 inches long and moves from 12 to 8 oclo…
The minute hand moves $12\pi$ inches. The minute hand moves approximately $37.70$ inches.
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3. draw both a line that is parallel and a line that is perpendicular t…
To draw the parallel line: Start at the given point, use a slope of - 2 (move 1 unit right and 2 units down to plot additional points and then draw the line). To draw the perpendi…
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find the midpoint of the line segment joining the points p₁ and p₂. p₁=…
$(6,1)$
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polygon s is a scaled copy of polygon r. what is the value of t?
\(100\)
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a water wheel has a radius of 12 feet. the wheel is rotating at 20 revo…
1508
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polygon q is a scaled copy of polygon p. what scale factor takes polygo…
$\frac{1}{2}$
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1. find the slope of the line that is parallel to y = -\\frac{3}{4}x + …
The slope of the parallel line is $-\frac{2}{3}$ and the slope of the perpendicular line is $\frac{3}{2}$.
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quadrilateral i is a scaled copy of quadrilateral h. what is the value …
$\frac{1}{2}$
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pentagon h is a scaled copy of pentagon g. pentagon g pentagon h what s…
$1.25$
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part b how does the narrators perspective most clearly help meet the au…
D. ringed
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find the distance between (8,4) and (9,-2) * your answer find the midpo…
Distance: $\sqrt{37}$ Mid - point: $(8.5,1)$
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in 6 - 8, determine whether each conjecture is true or false. give a co…
6. False. Counter - example: ∠ABC = 30°, ∠CBD = 150° 7. False. Counter - example: Two adjacent angles in a right - angled corner (e.g., 30° and 60°) 8. True
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quadrilateral n is a scaled copy of quadrilateral m. what scale factor …
$1.4$
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find the graph of the point (-3, -1).
The first graph (the one on the left) represents the point $(-3,-1)$ as it has the point 3 units to the left of the origin and 1 unit down.
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find the graph of the point (-1, 3).
The right - hand graph (the one where the point is 1 unit to the left of the y - axis and 3 units above the x - axis)
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triangle b is a scaled copy of triangle a. what is the value of c? tria…
33
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triangle x is a scaled copy of triangle w.
12
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find the missing side length (include units). round to the nearest hund…
\(18.52\) mi
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quadrilateral l is a scaled copy of quadrilateral k. quadrilateral k qu…
$\frac{7}{6}$
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convert the following angle in degrees to radians. 70° 70° = radians (s…
$\frac{7\pi}{18}$
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find the missing side length (include units). round to the nearest hund…
16.15 yd, 1.96 m
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pentagon t is a scaled copy of pentagon s. pentagon s pentagon t what i…
$1.8$
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find the value of b. pythagorean theorem: a² + b² = c² 5 in 12 in b b =…
$\sqrt{119}$
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find the value of a. pythagorean theorem: $a^{2}+b^{2}=c^{2}$ a 12 in 7…
$\sqrt{95}$ in
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example 4 triangle jkl has coordinates j(-1, 5), k(1, 2), and l(-3, -1)…
11. $J'(-1,-5),K'(1,-2),L'(-3,1)$ 12. $J''(1,5),K''(-1,2),L''(3,-1)$ 13. $J'''(4,1),K'''(6,-2),L'''(2,-5)$
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find a cofunction with the same value as the given expression. sin 8° s…
E. $\cos82$
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find the value of b. pythagorean theorem: a² + b² = c² b = √?
$\sqrt{51}$
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find the missing side length (include units). round to the nearest hund…
14 km 8.83 yd
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find the value of b. pythagorean theorem: a^2 + b^2 = c^2 b = \\sqrt{?}…
$\sqrt{161}$
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the angular speed of a point on a planet is $\frac{9pi}{10}$ radian per…
5655
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quadrilateral l quadrilateral m what scale factor takes quadrilateral l…
$\frac{5}{4}$
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which angle is congruent to ∠1?
∠3
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tess says this shape is a rhombus. jack says the shape is a square. who…
A rhombus is a quadrilateral with 4 sides the same length. A square is a quadrilateral with 4 sides the same length and 4 right - angles (square corners). Jack is correct.
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rectangle y is a scaled copy of rectangle x. what scale factor takes re…
$\frac{7}{8}$
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triangle h triangle i what is the value of g?
\(19^{\circ}\)
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which angle is adjacent to ∠4?
∠5
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what is the vertex? (-5,-2) (5,2) (-2,-5) (-5,2)
D. (-5,2)
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in the accompanying diagram, lines a and b are parallel, and lines c an…
Angle 2 and Angle 6
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triangle y is a scaled copy of triangle x. what scale factor takes tria…
$0.5$
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use the pythagorean theorem to find the length of the missing side of t…
\(\sin\theta=\frac{3}{5}\) \(\cos\theta=\frac{4}{5}\) \(\tan\theta=\frac{3}{4}\) \(\csc\theta=\frac{5}{3}\) \(\sec\theta=\frac{5}{4}\) \(\cot\theta=\frac{4}{3}\)
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13 a diagram of a poster board can be seen below. max wants to cover on…
162
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find the missing side length (include units). round to the nearest hund…
14.82 mi 37 mi
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question 1 - 3 (ma 912 gr 4 5) the volume of a basketball is 434 in³. s…
7.4 inches
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in the accompanying diagram, line n is parallel to line m, line t is a …
\(24^{\circ}\)
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pentagon y is a scaled copy of pentagon x. what is the value of z?
135
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solve each inequality below. graph the solution on a number line. 8. 2x…
8. Solution: $x < 4$, Graph: Open - circle at 4, shade left. 9. Solution: $x\geq - 2$, Graph: Closed - circle at - 2, shade right. 10a. 16 10b. 10
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convert the angle in degrees to radians. round to two decimal places. 2…
$4.40$
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hexagon j hexagon k what scale factor takes hexagon j to hexagon k?
$2.5$
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use the given triangle to evaluate the expression. if necessary, expres…
$0$
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a triangle has these properties: three sides of different lengths; two …
scalene, obtuse
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hexagon z is a scaled copy of hexagon y. what is the value of x?
$154$
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find the missing side length (include units). round to the nearest hund…
The first side length is \(21\) mi and the second side length is \(16\) m.
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brady jogs laps around a circular park with a fountain at the center. w…
The third table (where time values are 0, 2, 4, 6, 8 and distance values are all 50) could represent Brady's distance from the fountain.
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find the missing side length (include units). round to the nearest hund…
17 yd
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16 multiple choice 1 point what two dimensions can the front view show?…
B. Length, Height
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what is the measure of angle x? 73° a 163° b 34° c 107° d 17°
D. 17°
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trapezoid r is a scaled copy of trapezoid q. what is the value of s?
\(85\)
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(9x + 2)° 133°
\(x = \frac{131}{9}\)
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14 multiple choice 1 point what two dimensions can the top view show? w…
C. Length, Width
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u, shown in the coordinate plane below, is translated up 4 units and ri…
D. \((1,1)\)
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the shape of a water tower can partially be modeled by a sphere in whic…
2827
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if m∠4 = 119, what is m∠10? (not drawn to scale)
A. 119
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what is the vertex? (-1,-3) (3,1) (1,-3) (-1,-1)
C. (1,-3)
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parallelogram p what is the value of r? parallelogram q
26
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two cities, a and b, are 7000 miles apart. the radius of the earth is a…
$\theta = 1.75$ radians $\theta\approx100.27^{\circ}$
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what is the name of this shape? use the drop - down menus to explain yo…
The shape has 4 sides. Two sides of the shape are parallel. The other two sides are non - parallel. So, the shape is a trapezoid.
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2\\frac{1}{2} 6\\frac{1}{4} 1\\frac{3}{4} a triangle b triangle c
$4\frac{3}{8}$
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find a positive angle less than 360° that is coterminal with the given …
35
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in parallelogram lmno, what is the measure of angle n? 50° 70° 110° 130°
C. $110^{\circ}$
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explain how an object can have a negative position in a coordinate syst…
Position in a coordinate system is relative to an origin. Negative positions are in the opposite direction of the defined positive - direction from the origin.
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the perimeter of parallelogram wxyz is 50 millimeters. what is wz? (2x …
2 mm
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1. ad ≅ bc; ad || bc 1. given 2. ∠cad and ∠acb are alternate interior ∠…
CPCTC
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enrichment for math 1 examining points on lines name nia escobar date 1…
a) (Draw dots on (-2, 4), (0, 2), (2, 0) on the given graph) b) | x | y | |----|----| | -2 | 4 | | 0 | 2 | | 2 | 0 | c) Decreasing by 2 for every increase of 2 in x d) Increasing …
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in the diagram, the measure of ∠1 is 55°. if line y is rotated 5° clock…
$50^{\circ}$
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k is the midpoint of $overline{jl}$. what are the coordinates of l? k(7…
A. $(3,6)$
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what is the radius of the circle? 6 cm a 12 cm b 36 cm c 3 cm d 4 cm
C. 3 cm
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wyatt mows lawns to earn money. he charges by the area of the yard. a n…
C. $7,000\ ft^{2}$
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express the following statement as an equation involving the indicated …
$V=\frac{4}{3}\pi r^{3}$
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transformations in the plane · practice examples 1 and 2 identify the t…
1. Reflection 2. Translation 3. Translation 4. Reflection 5. Rotation 6. Rotation
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question: consider the function y = 2sin(x) for 0° ≤ x ≤ 360°. 1. graph…
The key points are $(0,0),(90,2),(180,0),(270,-2),(360,0)$. Plot these points and draw a smooth sine - wave curve on the coordinate plane with appropriate axis labels.
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what is the measure of ∠4? a 138° b 52° c 42° d 48°
A. $138^{\circ}$
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what is the circumference of this circle? use 3.14 for π. 12 cm 22.15 c…
37.68 cm
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write the inequality solution for each graph shown. use x as the variab…
6. $x > 4$ 7. $x\leq4$
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two parallel lines are cut by a transversal as shown below. suppose m∠5…
$m\angle2 = 148^{\circ}$, $m\angle4 = 32^{\circ}$