#### Chapter 5 Geometry

Section 5.7 Final Test

# 5.7.1 Final Test Module 5

This is a test for submission:
• Unlike open exercises, no hints for formulating mathematical expressions are provided.
• The test can be restarted or interrupted at any time.
• The test can be terminated and submitted using the buttons at the end of the page, or reset.
• The test can be attempted several times. Only the last version will be included in the statistics.

##### Exercise 5.7.1
Identify the figures below as precisely as possible by specifying the name of the type (preceded by an adjective if necessary) and describing as many properties of the figure as possible.

 Figure: Description of the Type: ${F}_{1}$ ${F}_{2}$ ${F}_{3}$ ${F}_{4}$ ${F}_{5}$

##### Exercise 5.7.2
Are the following results and statements right or wrong?
 right? Every rectangle is a rhombus. Every square is a parallelogram. There exists exactly one square with a diagonal of $5 \mathrm{cm}$. A triangle with the angles $36{}^{\circ }$ and $54{}^{\circ }$ is right-angled. In a rectangle the sum of all (interior) angles in radian measure is equal to $4\pi$.

##### Exercise 5.7.3
Consider a triangle ABC with side lengths $a=5 \mathrm{cm}$, $b=6 \mathrm{cm}$, and $c=9 \mathrm{cm}$. On the side $c$ a point $P$ and on the side $b$ a point $Q$ are chosen such that $\mathrm{PQ}$ is parallel to the side $a$ and $\left[\stackrel{‾}{PQ}\right]=0.50 \mathrm{cm}$. Calculate the lengths of the line segments $\left[\stackrel{‾}{PB}\right]$ and $\left[\stackrel{‾}{QC}\right]$ specified in centimetre.
1. $\left[\stackrel{‾}{PB}\right]$$=$
$\mathrm{cm}$
2. $\left[\stackrel{‾}{QC}\right]$$=$
$\mathrm{cm}$

##### Exercise 5.7.4
Consider a square with sides of length $a$. Find the formulas for the area and the circumference for the largest circle inscribed to the square as well as for the smallest circle containing the square completely:
1. Circumference of the circle within the square as a function of the side length $a$:
2. Area of the circle within the square as a function of the side length $a$:
3. Circumference of the circle around the square as a function of the side length $a$:
4. Area of the circle around the square as a function of the side length $a$:

Do not enter any brackets or radical terms. Enter, for example, ${2}^{0.5}$ instead of $\sqrt{2}$ to avoid the radical.

The test evaluation will be displayed here!