📐 geometry

1. **Stating the problem:** We are given a zigzag line with 5 points labeled 1 through 5 and some angles: $m\angle 1 = 88^\circ$, $m\angle 3 = 81^\circ$, and $m\angle 5 = 64^\circ$

1. The problem is to find the hypotenuse $a$ of a right triangle where the legs are $\sqrt{10}$ and $\sqrt{6}$.\n\n2. According to the Pythagorean theorem, for a right triangle wit

1. **Stating the problem:** We are given a zigzag line with 5 segments and several angles: 88°, 92°, 81°, and 64°. We need to find the measures of angles $m\angle 1$, $m\angle 2$,

1. The problem asks for the area of a shape denoted as $S$. 2. To find the area, we need to know the shape and its dimensions or a formula that applies to $S$.

1. **State the problem:** We have a right triangle with legs of lengths $\sqrt{10}$ and $\sqrt{6}$, and we want to find the length of the hypotenuse. 2. **Formula used:** In a righ

1. **State the problem:** We have a right triangle with legs of lengths 8 and 6, and we want to find the length of the hypotenuse $a$. 2. **Formula used:** In a right triangle, the

1. **Stating the problem:** We are given a right triangle with side lengths 3, 4, and 5. We need to find the area $S$ of this triangle.

1. **Problem Statement:** We have an isosceles triangle with an altitude drawn from the vertex to the base, forming two congruent right triangles. The altitude length is 18 inches,

1. **State the problem:** We have a ladder leaning against a building. The ladder is 28 feet long, and the building is 15 feet tall. We want to find the distance from the bottom of

1. **Problem Statement:** We need to explain why angles 2 and 3 are congruent. 2. **Given Information:**

1. **Énoncé du problème :** Trouver l'équation d'une ellipse centrée à l'origine dont un foyer est au point $\left(0, \sqrt{7}\right)$ et la distance entre deux points de l'ellipse

1. **State the problem:** We need to determine which triangles with given side lengths are right triangles. 2. **Formula used:** For a triangle with sides $a$, $b$, and $c$ (where

1. **State the problem:** We need to determine if triangle \(\Delta ABC\) with sides \(AB=10\), \(AC=18.75\), and \(BC=28.25\) is a right triangle. 2. **Recall the Pythagorean theo

1. **Stating the problem:** We have a triangle with three internal angles labeled as $z^\circ$, $y^\circ$, and $x^\circ$. Given are some external angles and one internal angle $X =

1. **State the problem:** Find the perimeter of triangle GIH with vertices at $G(-7,-8)$, $I(-3,-1)$, and $H(-1,-8)$. 2. **Formula:** The perimeter is the sum of the lengths of all

1. The problem is to find the measure of the angle indicated on the semicircular protractor. 2. A semicircular protractor measures angles from 0° to 180° along its curved edge.

1. **State the problem:** We need to find the area of an L-shaped figure composed of two rectangles joined at right angles. 2. **Identify the rectangles:** The larger rectangle has

1. **State the problem:** We have a right triangle formed by the TV tower, the guy wire, and the distance from the stake to the base of the tower. The tower height is 12 m, the guy

1. **Problem statement:** Given squares on the sides of triangles with some areas known and some unknown, determine if the triangles are right triangles and find missing areas or s

1. **State the problem:** We have a triangle with 3 sides, each 5 ft long, and we want to find its area in square feet. 2. **Identify the type of triangle:** Since all sides are eq

1. **Stating the problem:** We have a trapezoid JKMN with area 136 square kilometers. We want to find the area of triangle JKN formed by points J, K, and N. 2. **Understanding the