📐 geometry

1. **Problem:** Determine if the side lengths 10 ft, 12 ft, and 25 ft can form a triangle. 2. **Triangle Inequality Theorem:** For any triangle with sides $a$, $b$, and $c$, the fo

1. **Problem Statement:** Find the measure of angle $\angle QNS$ given the angles around point $N$ and $Q$ with labels $2a^\circ$, $b^\circ$, $108^\circ$, and $(a+b)^\circ$ as show

1. **State the problem:** We are given two intersecting lines forming vertical angles. One angle measures 75° and the opposite vertical angle measures (5x)°. 2. **Formula and rule:

1. **State the problem:** We are given two vertical angles formed by intersecting lines. One angle measures 130° and the other measures (3x - 20)°. We need to write an equation to

1. The problem involves completing figures by reflecting points across given lines of symmetry. 2. For each figure, identify a point not on the line of symmetry and count the numbe

1. **State the problem:** We have two intersecting lines forming two angles: one is 130° and the other is (3x - 20)°. We need to write an equation to find the value of $x$. 2. **Im

1. **Problem:** Classify the triangle with sides 6 in, 4 in, and 8 in by its angles and sides. 2. **Formula and rules:**

1. **Problem statement:** Find the value of $x$ for the triangle with area 30 ft², base $(x+4)$ ft, and height $x$ ft. 2. **Formula:** Area of a triangle is given by $$\text{Area}

1. **Problem statement:** We have a right triangle with a vertical side labeled $x\sqrt{3}$, a horizontal base divided into three segments: the left base angle is $45^\circ$, the r

1. **State the problem:** We need to find how much greater the surface area of the whole prism is compared to the shaded prism (the prism with the notch removed). 2. **Understand t

1. **State the problem:** We need to find the surface area of a rectangular pyramid with base dimensions 20 cm by 10 cm and slant heights 20 cm, 20.6 cm, and 22.4 cm for the triang

1. **Stating the problem:** We have a right triangle with the top horizontal side split into two segments of lengths 20 and 15, and a perpendicular segment $x$ dropping from the sp

1. **Problem 16:** Solve for $x$ in the right triangle with given sides 8 and 15. 2. The problem likely involves the Pythagorean theorem: $$a^2 + b^2 = c^2$$ where $c$ is the hypot

1. **State the problem:** We need to find the values of $x$ and $y$ in the given geometric figure involving triangle $ACX$ with points $B$, $D$, and $F$ on the sides and segments a

1. **State the problem:** We have a triangle L C X with points B on L C and D on C X. Segment B D is 3 m, B C is 7 m, D X is 1.4 m, and X Y is 18 m. We need to find the values of $

1. **State the problem:** We need to find the area of a triangular lot with sides 188 ft, 87 ft, and 167 ft, then calculate the cost at 3 per square foot. 2. **Formula used:** Use

1. The problem asks to find the cost of a triangular lot with sides 140 ft, 65 ft, and 111 ft, given the price is 3 per square foot. 2. To find the cost, we first need the area of

1. **State the problem:** Find the perimeter of triangle VUW with vertices V(-5,7), U(0,6), and W(0,-1). 2. **Formula:** The perimeter of a triangle is the sum of the lengths of it

1. **Problem Statement:** Find the missing angle measures $m\angle 1$, $m\angle 2$, and $m\angle 3$ for problems 5 and 6 in the quadrilaterals. 2. **Important Rule:** The sum of in

1. The problem gives a quadrilateral with angles $x^\circ$, $78^\circ$, and two right angles ($90^\circ$ each). The sum of interior angles in any quadrilateral is $360^\circ$. 2. U

1. **Problem 1:** Find the missing angle $x$ in a quadrilateral with angles $x$, $78^\circ$, and $x=192^\circ$ given. 2. **Problem 2:** Find the missing angle $x$ in a quadrilatera