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5.17: Area and Perimeter of Rhombuses and Kites
https://k12.libretexts.org/Bookshelves/Mathematics/Geometry/05%3A_Quadrilaterals_and_Polygons/5.17%3A_Area_and_Perimeter_of_Rhombuses_and_Kites
Area is half the product of the diagonals; perimeter is the sum of the sides. If we move the two triangles on the bottom of each quadrilateral so that they match up with the triangles above the horizo...Area is half the product of the diagonals; perimeter is the sum of the sides. If we move the two triangles on the bottom of each quadrilateral so that they match up with the triangles above the horizontal diagonal, we would have two rectangles. So, the height of these rectangles is half of one of the diagonals and the base is the length of the other diagonal. To find the perimeter, you must find the length of each side, which would be the hypotenuse of one of the four triangles.
2.1: Basic Visual Patterns
https://k12.libretexts.org/Bookshelves/Mathematics/Geometry/02%3A_Reasoning_and_Proof/2.01%3A_Basic_Visual_Patterns
The answer for the pattern rule is: to get the next step in the pattern, take the previous step and add another row of small triangles to the bottom with 2 more triangles than the row above it. The an...The answer for the pattern rule is: to get the next step in the pattern, take the previous step and add another row of small triangles to the bottom with 2 more triangles than the row above it. The answer is that the pattern rule is to get the number of squares in the next step in the pattern, take the number of squares in the previous step and divide by 2.
8.11: Rotation Rules
https://k12.libretexts.org/Bookshelves/Mathematics/Geometry/08%3A_Rigid_Transformations/8.11%3A_Rotation_Rules
In order to write the notation to describe the rotation, choose one point on the preimage (the yellow diamond) and then the rotated point on the green diamond to see how the point has moved. In order ...In order to write the notation to describe the rotation, choose one point on the preimage (the yellow diamond) and then the rotated point on the green diamond to see how the point has moved. In order to write the notation to describe the transformation, choose one point on the preimage (purple and blue diagram) and then the transformed point on the orange and blue diagram to see how the point has moved.
9.17: Volume of Pyramids
https://k12.libretexts.org/Bookshelves/Mathematics/Geometry/09%3A_Solid_Figures/9.17%3A_Volume_of_Pyramids
They carefully measure the width of the square base of the sand pyramid which is 4 feet and the height of the pyramid which is 5 feet. To find the volume of the pyramid, take the area of the base, \(B...They carefully measure the width of the square base of the sand pyramid which is 4 feet and the height of the pyramid which is 5 feet. To find the volume of the pyramid, take the area of the base, $B$ and multiply it times the height and then multiply it by $\dfrac{1}{3}$ . Next, plug the area of the base, and the height of the pyramid into the formula for volume of a pyramid and multiply the values together.
4.31: Converse of the Pythagorean Theorem
https://k12.libretexts.org/Bookshelves/Mathematics/Geometry/04%3A_Triangles/4.31%3A_Converse_of_the_Pythagorean_Theorem
The Pythagorean Theorem states that for a right triangle the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. The Converse of the Pythag...The Pythagorean Theorem states that for a right triangle the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. The Converse of the Pythagorean Theorem states that if the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the angle opposite the longest side is a right angle.
5.5: Area of Squares and Rectangles
https://k12.libretexts.org/Bookshelves/Mathematics/Geometry/05%3A_Quadrilaterals_and_Polygons/5.05%3A_Area_of_Squares_and_Rectangles
To find the area of a rectangle, use the measurements for length and width instead of side length. The label for area of a rectangle is similar to the label for area of a square from above. Find the a...To find the area of a rectangle, use the measurements for length and width instead of side length. The label for area of a rectangle is similar to the label for area of a square from above. Find the area of a rectangle with a length of 7\text{ ft }. and a width of 4\text{ ft }. Find the area of a rectangle with a length of 6 feet and a width of 5 feet. Find the area of a rectangle with a length of 9 meters and a width of 8 meters.
4.41: Special Right Triangles and Ratios
https://k12.libretexts.org/Bookshelves/Mathematics/Geometry/04%3A_Triangles/4.41%3A_Special_Right_Triangles_and_Ratios
Note that the order of the side ratios $x$ , $x\sqrt{3}$ , $2x$ and $x$ , $x$ , $x\sqrt{2}$ is important because each side ratio has a corresponding angle. The Pythagorean Theorem is a mathematica...Note that the order of the side ratios $x$ , $x\sqrt{3}$ , $2x$ and $x$ , $x$ , $x\sqrt{2}$ is important because each side ratio has a corresponding angle. The Pythagorean Theorem is a mathematical relationship between the sides of a right triangle, given by $a^2+b^2=c^2$ , where a and b are legs of the triangle and c is the hypotenuse of the triangle.
2.4: Reasoning Types
https://k12.libretexts.org/Bookshelves/Mathematics/Geometry/02%3A_Reasoning_and_Proof/2.04%3A_Reasoning_Types
This is an example of inductive reasoning, since we started with a number of specific observations, namely the $1^{st}, 2^{rd}, 3^{rd}, 4^{nd}$ , and so on numbers in a sequence, and use the observat...This is an example of inductive reasoning, since we started with a number of specific observations, namely the $1^{st}, 2^{rd}, 3^{rd}, 4^{nd}$ , and so on numbers in a sequence, and use the observations to make the statement that the pattern is to add 3n, where n is the count, to each number to get the next: $1+3(1)=4, 4+3(2)=10, 10+3(3)=19, 19+3(4)=31$ , and so on.
5.26: Determine Missing Angle Measures
https://k12.libretexts.org/Bookshelves/Mathematics/Geometry/05%3A_Quadrilaterals_and_Polygons/5.26%3A_Determine_Missing_Angle_Measures
$\begin{aligned} 295^{\circ}+\angle M &=360^{\circ} \\ 295^{\circ}−295^{\circ}+\angle M &=360^{\circ}−295^{\circ} \\ \angle M &=65^{\circ} \end{aligned}$ \(\begin{aligned} 44^{\circ}+\angle C&=180^{... $\begin{aligned} 295^{\circ}+\angle M &=360^{\circ} \\ 295^{\circ}−295^{\circ}+\angle M &=360^{\circ}−295^{\circ} \\ \angle M &=65^{\circ} \end{aligned}$ $\begin{aligned} 44^{\circ}+\angle C&=180^{\circ} \\ 44^{\circ}−44^{\circ}+\angle C&=180^{\circ}−44^{\circ} \\ \angle C &=136^{\circ} \end{aligned}$
5.2: Rectangles
https://k12.libretexts.org/Bookshelves/Mathematics/Geometry/05%3A_Quadrilaterals_and_Polygons/5.02%3A_Rectangles
Identify the properties of rectangles. Determine lengths of missing sides. Video: Overview of Squares and Rectangles Practice: Rectangles
6.6: Circle Area
https://k12.libretexts.org/Bookshelves/Mathematics/Geometry/06%3A_Circles/6.06%3A_Circle_Area
If r is the radius of a circle, then its area is $A=\pi r^2$ . If the area of a circle is $20\pi \text{ units }$ , what is the radius? The diameter of the circle is the same as the length of a side ...If r is the radius of a circle, then its area is $A=\pi r^2$ . If the area of a circle is $20\pi \text{ units }$ , what is the radius? The diameter of the circle is the same as the length of a side of the square. The area of the shaded region would be the area of the square minus the area of the circle. First, use the formula for the area of a circle to solve for the radius of the circle. The length of a diameter is two times the length of a radius.

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