Welcome to your ACT 1 Geo: Apply the triangle inequality

$Q_{1}:$ Which sets of numbers could be the lengths of sides of a triangle?

$Q_{2}:$ It is possible to have a triangle with all of the following sets of sides EXCEPT

$Q_{3}:$ In $\Delta ABC$, $AB = 4$ and $BC = 7$. If the length of the third side is an integer, then what is the greatest possible value for $AC$?

$Q_{4}:$ For how many integer values of $x$ can $6, 8,$ and $x$ be the lengths of the three sides of a triangle?

Hint

$Q_{5}:$ The lengths of the sides of a triangle are $3, 5,$ and $x$. How many possible values of $x$ are there?

Hint

$Q_{6}:$ The lengths of two sides of a right triangle are $15$ and $17$. Which of the following could be the length of the third side?

$Q_{7}:$ If the difference between the measures of the two acute angles of a right triangle is $20$, what is the measure, in degrees, of the smaller one?

$Q_{8}:$ If one side of $\Delta ABC$ is $5$, what is the smallest integer that could be the perimeter of the triangle?

$Q_{9}:$ In triangle $ABC$, $AB = BC$. If angle $B$ contains $x$ degrees, find the number of degrees in angle $A$.

$Q_{10}:$ If a triangle has side lengths of 7, 7, and 13, what type of triangle is it?

$Q_{11}:$ If $ a, b,$ and $c$ are the side lengths of the triangle, then one of the following inequality is true?

$Q_{12}:$ In a triangle $ABC$ If $A<B<C$, then

$Q_{13}:$ Which of the following expresses the possible values of $p$, if $p$ is the perimeter of $RST $?

$Q_{14}:$ An isosceles triangle has sides of lengths $5, 11,$ and $x$. How many possible values of $x$ exist?

$Q_{15}:$ The distance between points $A$ and $D$ is $6$, and the distance between $D$ and $F$ is $4$. Which of the following is NOT a possible value for the distance between $F$ and $A $?

$Q_{16}:$ In the figure below, $r$ must be

$Q_{17}:$ Two sides of a triangle have lengths $8$ and $4$. Find the largest possible integer lengths of the third side?

$Q_{18}:$ In triangle $ABC$, if $AB<AC$ and$m\angle C=30$, then $m\angle B$ must be

$Q_{19}:$ List the angles in order of smallest to largest.

$Q_{20}:$ List the sides in order of longest to shortest.

$Q_{21}:$ List the sides in order of smallest to largest.

$Q_{22}:$ Which of the following is true?

$Q_{23}:$ Given the $2$ angles shown, determine which side is the longest side of the triangle?

$Q_{24}:$ Given $\Delta ABC$ as shown. Which statement is NOT true?

$Q_{25}:$ What conclusions can you draw about $x $?

Hint