📐 geometry

1. **State the problem:** We need to determine which transformation among the given options results in an image congruent to its pre-image. 2. **Recall the rule for congruence in t

1. **State the problem:** We have two triangles, JKL with vertices J(6,2), K(2,5), L(7,8) and MNO with vertices M(5,-8), N(1,-5), O(6,-2). We want to find which transformation maps

1. The problem is to understand how to solve problems involving a right angle, typically in geometry or trigonometry. 2. In a right angle triangle, one angle is exactly $90^\circ$.

1. The problem asks to rotate a figure around point A by a half turn (180 degrees) clockwise. 2. A half turn clockwise rotation means every point of the figure moves to a position

1. **Problem statement:** Given three points $A$, $B$, and $C$ in 3D space, find the equation of the plane $E$ passing through these points in coordinate form. 2. **Formula and rul

1. **Problem Statement:** We have a triangle ABC with vertex A at the top, B on the left, and C on the right. Inside triangle ABC, there are 4 individual smaller triangles that fit

1. **Problem Statement:** We have triangle $ABC$ with points $D$, $E$, and $F$ as midpoints of segments $AC$, $BD$, and $AE$ respectively. Given the area of triangle $BEF$ is 5, we

1. **Problem statement:** Given that lines $mn \parallel xy$ and angle $\widehat{ABy} = 60^\circ$, find angle $\widehat{BAm}$. Also, given that $At$ is the bisector of angle $nAB$

1. **State the problem:** We are given two transversals intersecting parallel lines with various angles labeled. We focus on Transversal Line 1 (red) to find the measurements of an

1. The problem asks to write the translation rule that maps quadrilateral QRST to quadrilateral Q'R'S'T'. 2. A translation moves every point of a figure the same distance in the sa

1. **Stating the problem:** We need to find the size of the reflex angle to the nearest degree given a protractor diagram with two rays forming an angle.

1. **State the problem:** Find the size of angle ABC to the nearest degree given a protractor diagram where vertex B is at the bottom center, ray BA is horizontal to the right, and

1. **State the problem:** Find the surface area of a cylinder with diameter 14.4 inches and height 15.6 inches. 2. **Formula for surface area of a cylinder:**

1. **State the problem:** Find the surface area of a cylinder with diameter 4.8 yd and height 2 yd. 2. **Formula:** The surface area $SA$ of a cylinder is given by

1. **Problem:** Work out the size of angle $q$ in the given hexagon-like shape with angles 120°, 120°, and 60° marked. 2. **Angle fact used:** The sum of angles around a point is 3

1. **State the problem:** We need to find the size of angle $q$ in the given hexagon-like shape and identify the angle fact used. 2. **Identify the angle fact:** The problem shows

1. **State the problem:** We have triangle ABC with angles $\angle A = 35^\circ$, $\angle B = 88^\circ$, and side $AC = 44$ mm. We need to find $m\angle C$, side $c$ (opposite $\an

1. **Stating the problem:** Identify the relationships between pairs of lines and pairs of angles in the given 3D figure and trapezoid. 2. **Lines pairs:**

1. **State the problem:** We have two similar triangles. The sides of the smaller triangle are 4 in and 13 in, and the corresponding sides of the larger triangle are $x$ and 22.75

1. **State the problem:** Given a triangle with sides $a=15$, $b=18$, and $c=20$, find the measure of angle $C$ opposite side $c$ using the Law of Cosines. 2. **Formula:** The Law

1. **State the problem:** We are given a triangle with sides $a=20$, $b=18$, and angle $C=15^\circ$. We need to find side $c$ using the Law of Cosines. 2. **Formula:** The Law of C