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10.7: Study Guide

Difficulty Level: At Grade Created by: CK-12

Keywords: Define, write theorems, and/or draw a diagram for each word below.

\begin{align*}1^{st}\end{align*}1st Section: Triangles and Parallelograms

Perimeter

Area of a Rectangle: \begin{align*}A = bh\end{align*}A=bh

Perimeter of a Rectangle \begin{align*}P = 2b + 2h\end{align*}P=2b+2h

Perimeter of a Square: \begin{align*}P = 4s\end{align*}P=4s

Area of a Square: \begin{align*}A = s^2\end{align*}A=s2

Congruent Areas Postulate

Area Addition Postulate

Area of a Parallelogram: \begin{align*}A = bh\end{align*}A=bh

Area of a Triangle: \begin{align*}A = \frac{1}{2} \ bh\end{align*}A=12 bh or \begin{align*}A = \frac{bh}{2}\end{align*}A=bh2

Homework:

\begin{align*}2^{nd}\end{align*}2nd Section: Trapezoids, Rhombi, and Kites

Area of a Trapezoid: \begin{align*}A = \frac{1}{2} h(b_1 + b_2)\end{align*}A=12h(b1+b2)

Area of a Rhombus: \begin{align*}A = \frac{1}{2} d_1 d_2\end{align*}A=12d1d2

Area of a Kite: \begin{align*}A = \frac{1}{2} d_1 d_2\end{align*}A=12d1d2

Homework:

\begin{align*}3^{rd}\end{align*}3rd Section: Area of Similar Polygons

Area of Similar Polygons Theorem

Homework:

\begin{align*}4^{th}\end{align*}4th Section: Circumference and Arc Length

\begin{align*}\pi\end{align*}π

Circumference: \begin{align*}C = \pi d\end{align*}C=πd or \begin{align*}C = 2 \pi r\end{align*}C=2πr

Arc Length

Arc Length Formula: length of \begin{align*}\widehat{A B} = \frac{m \widehat{A B}}{360^\circ} \cdot \pi d\end{align*} or \begin{align*}\frac{m \widehat{A B}}{360^\circ} \cdot 2 \pi r\end{align*}

Homework:

\begin{align*}5^{th}\end{align*} Section: Area of Circles and Sectors

Area of a Circle: \begin{align*}A = \pi r^2\end{align*}

Sector

Area of a Sector: \begin{align*}A = \frac{m \widehat{A B}}{360^\circ} \cdot \pi r^2\end{align*}

Segment of a Circle

Homework:

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CK.MAT.ENG.SE.1.Geometry-Basic.10.7