Welcome to your ACT 1 Geo: Use relationships involving medians

$Q_{1}:$ A segment extending from one vertex to the midpoint of the opposite side is ?

$Q_{2}:$ Given $\Delta RST$ has an exterior altitude, the triangle could be which of the following?

$Q_{3}:$ Given $\Delta MNL$, the measure of $\angle NMP$ is $40$. $ \overline{MP}$ bisects $\angle M$, and $\angle N$ is congruent to $\angle LMP$. Find $m \angle L$.

$Q_{4}:$ In $\Delta QRS$, $\overline{RT}$ is an altitude Which additional condition would not be sufficient to prove that $QR=SR$?

$Q_{5}:$ The sides of a right triangle are $6, 8,$ and $10$. Find the altitude drawn to the hypotenuse.

$Q_{6}:$ In a parallelogram whose area is $15$, the base is represented by $x + 7$ and the altitude is $x – 7$. Find the altitude of the parallelogram.

$Q_{7}:$ Find the altitude of an equilateral triangle whose side is $20$.

$Q_{8}:$ What is the area of an equilateral triangle whose altitude is $6$?

$Q_{9}:$ In the figure below, regular hexagon $ABCDEF$ is inscribed in rectangle $PQRS$. If each side of the hexagon is $1$, what is the area of the rectangle?

$Q_{10}:$ Let $(0, 0)$ and $(−2, 2)$ are the coordinates of two vertices of an equilateral triangle. Which of the following could be the coordinates of the third vertex?

$Q_{11}:$ If $\overline{AB} \perp \overline{CD}$ and $\overline{AB}$ bisects $\overline{CD}$, then

$Q_{12}:$ In figure below, $Y,L$ and $G$ are midpoints of $PK, KQ$ and $PQ$, respectively. Find $x$.

$Q_{13}:$ In figure below, $Y,L$ and $G$ are midpoints of $PK, KQ$ and $PQ$, respectively. Find $y$.

$Q_{14}:$ If $\overline{AD}$ is a midpoint. what is the value of $x$?

$Q_{15}:$ In the figure below, find the coordinates of the orthocenter of $\Delta JKL$

Hint

$Q_{16}:$ What is the slope of the line that contains the altitude through vertex $V$ of $\Delta OAV$?

$Q_{17}:$ In $\Delta WAH$, $overline{WP}$ is a median and an angle bisector, m$\angle HWP=r+12$, m$\angle PAW=3r-2$, and m$\angle HWA=4r-16$. What is the m$\angle WPH$?

$Q_{18}:$ In $\Delta ABC$, $overline{AQ}$ is a perpendicular bisector, m$\angle ACB=8t+17$ and m$\angle CAQ=10+t$. What is the value of $t$?

$Q_{19}:$ In $\Delta GHJ$, $HP=5z-16$, $PJ=3z+8$. Find $HJ$ if $\overline{GP}$ is a median?

$Q_{20}:$ In $\Delta GHJ$, let $\overline{HM}$ is an altitude and $\angle HMG = 4z + 14$ , find the value of $z$.

$Q_{21}:$ In $\Delta GHJ$, $m\angle GJN = 6y - 3$, $m\angle NJH = 4y + 23$, Find $m\angle GJH$ if $\overline{JN}$ is an angle bisector.

$Q_{22}:$ In the diagram, $JK$ is the perpendicular bisector of $NL$. Find $NK$.

$Q_{23}:$ In a triangle, which line segment connects a vertex to the midpoint of the opposite side and divides the triangle into two equal areas?

$Q_{24}:$ You are given a quadrilateral with two pairs of congruent sides. What type of line segment is guaranteed to pass through the intersection of the diagonals of this quadrilateral?

$Q_{25}:$ In a triangle, which line segment connects a vertex to the opposite side in such a way that it is equidistant from the other two sides of the triangle?

$Q_{26}:$ In a triangle, which line segment is perpendicular to a side and passes through the opposite vertex?

$Q_{27}:$ You are given a triangle with an angle bisector drawn from one vertex to the opposite side. What is the relationship between the lengths of the two segments into which the angle bisector divides the side?

$Q_{28}:$ In a quadrilateral, what type of line segment is guaranteed to be perpendicular to both diagonals and pass through their point of intersection?