📐 geometry

1. **State the problem:** Tammy mapped quadrilateral $ABCD$ onto quadrilateral $FGHE$ using a reflection and a translation and concluded the figures are congruent.

1. **Problem Statement:** We need to find the line of reflection that maps $\triangle ABC$ onto $\triangle A'B'C'$. This line is the axis of symmetry between the two triangles. 2.

1. **State the problem:** We are given two triangles $\triangle ABC$ and $\triangle A'B'C'$ with coordinates:\n\n$A(-2,5)$, $B(3,3)$, $C(1,-1)$ and $A'(-7,5)$, $B'(-2,3)$, $C'(-4,-

1. **State the problem:** We need to determine which single transformation maps quadrilateral $A$ from the bottom-right area of the grid to quadrilateral $B$ in the top-right area.

1. **State the problem:** Casey mapped line segment $UV$ onto line segment $ST$ using rigid transformations (translation and rotation) without dilation and concluded the segments a

1. **State the problem:** We have quadrilateral ABCD rotated about point Q to form A'B'C'D'. We need to determine the angles of rotation that map ABCD to A'B'C'D'.

1. **State the problem:** We are given two complementary angles \(\angle 1\) and \(\angle 2\) with measures \(m\angle 1 = (8x - 17)^\circ\) and \(m\angle 2 = (6x + 9)^\circ\). We n

1. \text{State the problem: We are given two complementary angles } \angle 1 \text{ and } \angle 2 \text{ with measures } m\angle 1=(3x-12)^\circ \text{ and } m\angle 2=(8x+3)^\cir

1. **State the problem:** We need to find the distance between Silver Mountain and Mount Clether given that Silver Mountain is 165 km west of Mount Clether at a bearing of 291°. 2.

1. **State the problem:** We have triangle MNO with vertices \(M(-3, -6)\), \(N(-8, -4)\), and \(O(-6, -2)\). We want to find the coordinates of these points after a 90 degree coun

1. **State the problem:** We have a rectangle with vertex $Q$ at coordinates $ (1, 6) $. We apply the translation rule $ (x, y) \to (x + 5, y + 2) $ to find the new coordinates of

1. **State the problem:** Determine if the first pair of polygons (A and B) is congruent to the second pair (B and A) based on their shapes and orientations. 2. **Understand congru

1. The problem asks about the volume, but no specific shape or dimensions are given. 2. Volume formulas depend on the shape: for example, for a cube, volume is $$V = s^3$$ where $s

1. **State the problem:** Find the surface area of a cone with radius $r=4$ and height $h=5$. 2. **Formula:** The total surface area $A$ of a cone is given by:

1. **Problem 1:** Given $m\angle PR = 115^\circ$, find the measure of arc $PNR$. - The angle $\angle PR$ is an inscribed angle that intercepts arc $PNR$.

1. **State the problem:** We have a circle with two secant segments $SU$ and $WU$ and a tangent segment $XU$ from point $U$ outside the circle.

1. **State the problem:** We need to find the area of quadrilateral $EFGH$ with sides $EH=8$ cm, $HG=11$ cm, and $FG=4$ cm, and right angles at $H$ and $F$. 2. **Analyze the shape:

1. **State the problem:** We need to find the perimeter of a triangle with a vertical height of $9$ cm and a base split into two segments of $2$ cm and $12$ cm, so the total base l

1. The problem states the Pythagorean theorem: $A^2 + B^2 = C^2$. 2. This formula relates the lengths of the sides of a right triangle, where $A$ and $B$ are the legs and $C$ is th

1. **State the problem:** Given that $\overline{MN} \parallel \overline{QR}$, prove that $\triangle MNP \sim \triangle QRP$.

1. **Problem Statement:**\nGiven a triangle $\triangle ABC$ where $AB = c$, $AC = b$, and $CB = a$, and the triangle is not a right triangle. We need to prove that $a^2 + b^2 \neq