📐 geometry

1. **Problem:** Josh draws 5 lines labeled A-E. Which two lines are parallel? 2. **Understanding parallel lines:** Parallel lines are lines in a plane that never meet; they have th

1. **Problem Statement:** Calculate the lateral surface area of a triangular prism with a base triangle having one side length of 9 m and a prism length (height) of 21 m. 2. **Form

1. **State the problem:** Calculate the total surface area of a rectangular box with length $90$ cm, width $60$ cm, and height $50$ cm. 2. **Formula:** The total surface area $A$ o

1. **Problem Statement:** Reflect the rectangle with vertices $A(1,2), B(4,5), C(7,2), D(4,-1)$ about the line $y=x+1$. 2. **Formula for Reflection about line $y=x+c$:**

1. **Problem Statement:** Create a Level 4 project demonstrating understanding of transformations and quadrilaterals. 2. **Transformations:** Level 4 requires at least 3 distinct t

1. **Problema:** Determinar algebraicamente si la línea $y = -3x$ es secante, exterior o tangente a la circunferencia $C: x^2 + y^2 = 14$. 2. **Fórmula y regla:** Para saber la rel

1. **State the problem:** Find the volume of a cone with base radius $r=4$ meters and height $h=9$ meters. 2. **Formula for the volume of a cone:**

1. The problem asks which set of side lengths will NOT form a triangle. 2. Recall the Triangle Inequality Theorem: For any triangle with sides $a$, $b$, and $c$, the sum of the len

1. **Problem:** Find the volume of a triangular pyramid with base area 12 square meters and height 10 meters. 2. **Formula:** The volume $V$ of a pyramid is given by

1. **State the problem:** We are given two similar triangles, Triangle A with sides 8, 10, 10 and Triangle B with sides 12, 15, 15. We need to find the scale factor from Triangle A

1. **State the problem:** Calculate the area of the shaded region between two triangles using two different methods. 2. **Given data:**

1. **Stating the problem:** We have a right triangle XYZ with a right angle at Z, angle $\angle X = 69^\circ$, and side $YZ = 3$ (vertical side). We need to find the lengths $XY$,

1. **State the problem:** We have a right triangle DEF with a right angle at F, side DF = 4 units, and angle D = 63°. 2. **Find the missing parts:** We need to find DE, EF, and the

1. **Problem 1: Area of the trapezoid with a right triangle inside** Given dimensions: height $h=6$ m, bases $b_1=7.4$ m and $b_2=10.4$ m.

1. **Problem statement:** Find the area of the trapezoid at bottom-left. 2. **Formula for trapezoid area:**

1. **Problem Statement:** Given triangle ABC with segment DE parallel to BC and segment EF parallel to AB, and given lengths BC = 24, AC = 18, AB = 18, DE = 6, EF = 12, determine w

1. **Stating the problem:** We are given two triangles, \(\triangle DEF\) and \(\triangle ABC\), with \(\angle F \cong \angle C\) and right angles at \(D\) and \(A\) respectively.

1. **State the problem:** Find the angle $\angle XYZ$ in the given right triangle with vertices $X$, $Y$, and $Z$. 2. **Identify the sides:** From the description, the triangle $XY

1. **State the problem:** We need to find the height $h$ of a tree that casts a shadow 10 feet long, with the distance from the top of the tree to the end of the shadow being 26 fe

1. **State the problem:** We need to find the length of the cable, which forms the hypotenuse of a right triangle with legs 12 feet (flagpole height) and 6 feet (distance from base

1. **Problem:** Points A, B, and C are collinear. Given distances AB and BC, find AC. 2. **Formula:** Since points are collinear, the distance AC is the sum of AB and BC: