📐 geometry

1. The problem asks: How many vertices does a triangle have? 2. A vertex is a point where two sides of a polygon meet.

1. **Problem Statement:** Determine if the reason for congruence of two right triangles is always Hypotenuse-Leg (HL).

1. **Problem Statement:** We want to describe the five ways to prove that two triangles are congruent. 2. **The Five Congruence Theorems:**

1. **State the problem:** We need to find the length of the segment $AB$ on a number line where point $A$ is at $-3$ and point $B$ is at $4$. 2. **Formula used:** The length of a s

1. **State the problem:** We need to find the length of the segment $AB$ on a number line where $A$ is at $5$ and $B$ is at $9$. 2. **Formula used:** The length of a segment on a n

1. **State the problem:** We need to find the area of a triangle with base $9$ and height $9$. 2. **Formula for the area of a triangle:**

1. **State the problem:** We need to find the area of an isosceles triangle with a base of $9$ units and a height of $9$ units. 2. **Formula for the area of a triangle:** The area

1. **State the problem:** We need to find the area of a right triangle with a base of $7$ meters and a height of $10$ meters. 2. **Formula:** The area $A$ of a triangle is given by

1. **State the problem:** We are given two parallel lines $m$ and $n$ cut by a transversal $t$. We need to find the value of $x$ given the angles $(6x-8)^\circ$ and $(2x+4)^\circ$.

1. **State the problem:** We are given a triangle with angles labeled as $ (2x+12)^\circ $, $ 56^\circ $, and $ (9x-20)^\circ $. We need to find the measure of the smallest angle.

1. **State the problem:** Find the area of the L-shaped polygon with side lengths $10$, $14$, and $18$. 2. **Understand the shape:** The L-shaped polygon can be divided into two re

1. **State the problem:** We are given that ray $p$ bisects angle $a p c$. The measure of angle $a p b$ is $2x + 9$ and the measure of angle $a p c$ is $3x + 35$. We need to find t

1. **State the problem:** We are given three points $g$, $h$, and $I$ on a line with $h$ between $g$ and $I$. The distances are $g h = 2x - 9$, $h I = 14$, and $g I = 3x - 8$. We n

1. **State the problem:** We need to find the measure of the major arc $\overset{\frown}{ACB}$ given the central angle $146^\circ$ between points $A$ and $B$. 2. **Recall the rule:

1. **Problem Statement:** We need to find the measure of the arc $mACB$ in a circle where a central angle of $146^\circ$ and a right angle ($90^\circ$) are given. 2. **Understandin

1. **Problem:** Find the volume of a cube with edge length $8$ inches. 2. **Formula:** The volume $V$ of a cube with edge length $s$ is given by $$V = s^3$$

1. **Problem Statement:** We have triangle XYZ with vertices approximately at $X(4,5)$, $Y(4,3)$, and $Z(7,4)$. We need to perform three rotations of this triangle around point $Z$

1. **State the problem:** We start with point $A(3,4)$ and apply three transformations in order:

1. The problem asks about the relationship between the side lengths of Triangles 1 and 2 under a rigid transformation. 2. A rigid transformation preserves distances and angles, so

1. **Problem Statement:** We need to determine which sequence(s) of transformations (translations, rotations, reflections) take the lower left triangle of the Trinidad and Tobago f

1. The problem asks us to find the angle vertical to $\angle 4$ formed by two intersecting lines. 2. When two lines intersect, they form two pairs of vertical (opposite) angles. Ve