📐 geometry

1. **State the problem:** We are given two parallel lines $m$ and $n$ cut by a transversal, creating two angles: $(2x+22)^\circ$ and $(4x+2)^\circ$. We need to find the value of $x

1. **Problem Statement:** We want to understand what translation vectors are and see some examples.

1. **State the problem:** We need to find the shaded area inside rectangle $ABDC$ after removing two white triangular regions: triangle $AFD$ and triangle $FBG$. 2. **Given data:**

1. **State the problem:** We have triangle ABC with base $AB = 12$ cm and height $h = 10$ cm. The height is 2 cm shorter than the base, which matches since $12 - 2 = 10$. We need t

1. **State the problem:** We need to find the shaded area in a large right triangle with base $10$ cm and height $12$ cm, where a smaller right triangle is cut out on the left side

1. **State the problem:** We need to find the measure of angle $q$ in the given figure where $AD$ and $CF$ are straight lines. 2. **Identify given angles and lines:**

1. **State the problem:** We are given a figure with angles at point $O$. We know $\angle BOC = 66^\circ$ and $\angle COD$ is 3 times $\angle AOB$. We need to find $\angle COD$. 2.

1. **State the problem:** We have trapezium ABCD with one line of symmetry, where $DC = 47$ cm, $AD = 12$ cm, and $\angle ADC = 60^\circ$. We need to find the area of the trapezium

1. **State the problem:** We have trapezium ABCD with one line of symmetry, where $AD=12$ cm, $DC=47$ cm, and $\angle ADC=60^\circ$. We need to find the area of trapezium ABCD. 2.

1. **State the problem:** We have a figure composed of a rectangle and a semicircle. The area of the rectangle is given as $128\ \text{cm}^2$. We need to find the perimeter of the

1. **State the problem:** We have Polygon Q as a scaled copy of Polygon P with a scale factor of $\frac{1}{2}$. We need to find the fraction of Polygon Q's area compared to Polygon

1. **State the problem:** We have Triangle J, a right triangle with legs of lengths $4$ and $5$. James created Triangle K by scaling Triangle J by a factor of $4$. We need to find

1. **State the problem:** Determine if $\triangle VWX$ is similar to $\triangle YZX$ and explain why or why not. 2. **Identify given information:** The diagram shows two horizontal

1. **State the problem:** Given $m\angle 2 = 30$ and $m\angle 1 = 2m\angle 2$, prove that $m\angle 3 + m\angle 4 = 90$. 2. **Given information:**

1. **State the problem:** We need to find an angle adjacent to $\angle 2$ formed by two intersecting lines. 2. **Recall the definition:** Adjacent angles share a common side and a

1. **State the problem:** We need to find the angle supplementary to $\angle 4$. 2. **Recall the definition:** Two angles are supplementary if the sum of their measures is $180^\ci

1. **Problem Statement:** We have a triangle with a horizontal base split into two segments: $g$ on the left and $b$ on the right.

1. **State the problem:** We have a triangle with a left side length of $21$, a left base angle of $30^\circ$, a right base angle of $60^\circ$, and the base split into two segment

1. **Problem 6:** Identify the statements as contrapositive, converse, or inverse of the statement: "If two lines are perpendicular, then they intersect to form right angles." 2. *

1. **State the problem:** We are given two parallel lines $PQ$ and $AB$ cut by a transversal $PCB$. We know the angle at $P$ is $53^\circ$, the angle at $A$ is $37^\circ$, and we w

1. **State the problem:** We are given one angle of a linear pair as $120^\circ$ and need to find the measure of the other angle. 2. **Recall the property of a linear pair:** The s