📐 geometry

1. **State the problem:** We have a triangle with side lengths 6 mm, 6 mm, and 6 mm. We need to determine what kind of triangle it is. 2. **Recall triangle types based on side leng

1. The problem asks to classify a triangle with angles 89°, 32°, and 59°. 2. Recall the types of triangles by angles: equilateral (all angles 60°), isosceles (at least two equal an

1. The problem is to find the length of the unknown side $h$ in a right triangle where one leg is 22 and the hypotenuse is 26. 2. We use the Pythagorean theorem for right triangles

1. **State the problem:** Find the midpoint of the line segment with endpoints $(-6,9)$ and $(2,5)$. 2. **Formula:** The midpoint $M$ of a segment with endpoints $(x_1,y_1)$ and $(

1. Problem: Identify a transformation that can be used to prove $\triangle ABC \sim \triangle ADE$ by the AA similarity postulate given that $\angle A$ is congruent to itself by th

1. The problem asks for the coordinates, but it is unclear which coordinates are needed. 2. Coordinates usually refer to points in a plane or space, often given as $(x,y)$ in 2D or

1. **Nêu bài toán:** Cho tam giác ABC vuông tại A, đường cao AH (H thuộc BC). Gọi M và N lần lượt là trung điểm của AH và AC. Chứng minh rằng $$BN = BM \cdot \cos \angle ABC$$. 2.

1. **State the problem:** Calculate the perimeter of an L-shaped composite figure with sides 4 ft, 7 ft, 3 ft, 5 ft, and 12 ft. 2. **Formula:** The perimeter of a polygon is the su

1. The problem is to understand what a perpendicular bisector is. 2. A perpendicular bisector of a line segment is a line that divides the segment into two equal parts at a 90-degr

1. **Problem statement:** Given square ABCD with points K inside such that $AK = BK$ and angles $\angle KCB = \angle KDA = 75^\circ$, prove that triangle $\triangle AKB$ is equilat

1. **Problem statement:** Find the length DV, angle VDP, length VX (X midpoint of CD), angle VXP, and the vertical height of the smaller pyramid VEFGH given its volume 24 cm³.

1. **Problem statement:** We have a pyramid with a square base ABCD where each side is $\sqrt{72}$ cm.

1. **Problem statement:** (a) Find the measure of angle $x$ in a regular pentagon where three angles are labeled $x$.

1. **Problem Statement:** We have a shape with vertices A at (2,1) and B at (2,4). The shape is reflected about the line $y = -x$. We need to find the coordinates of the images of

1. **Problem Statement:** We have triangles A, B, and D on a coordinate plane with the line $y=x$. We need to find transformations mapping triangle A to D and B, and find the coord

1. **Problem Statement:** We have a large semi-circle with radius 7 cm and a smaller semi-circle with diameter 7 cm cut out and reattached. We need to find:

1. The problem states that O is the center of the circle, and we have two angles: one at the circumference (angle A) as $2x + 10$ and one at the center (angle O) as $x + 110$. 2. I

1. **Stating the problem:** We have a circle with center O and points A, B, C, D, E on the circumference. Given that the sum of the inscribed angles $\angle BDA + \angle BCA + \ang

1. Le problème demande de représenter graphiquement le segment d'extrémités $x$ et $y$ dans $\mathbb{R}^n$. 2. Par définition, le segment $[x,y]$ est l'ensemble des points $z$ tels

1. **Problem Statement:** Two non-congruent circles have centers at $C_1$ and $C_2$. Diameter $\overline{AB}$ of circle $C_1$ and diameter $\overline{CD}$ of circle $C_2$ are perpe

1. **Stating the problem:** We have a right triangle ABC with a right angle at B and angle A measuring 55°. 2. **Understanding the angles:** In any triangle, the sum of the interio