📐 geometry

1. **State the problem:** We need to show that the quadrilateral PATR with vertices \(P(-3,3)\), \(A(3,2)\), \(T(-4,-3)\), and \(R(2,-4)\) is a parallelogram by finding the lengths

1. **State the problem:** We need to find the perimeter of a square with side length 8 cm. 2. **Formula:** The perimeter $P$ of a square is given by the formula:

1. **Problem statement:** We have a triangular dog house with sides in the ratio 2:2:1, where the shortest side (base) is 1 meter. Inside, there is a smaller triangular storage are

1. The problem asks which angles are supplementary to \(\angle 6\). Supplementary angles are two angles whose measures add up to \(180^\circ\).\n\n2. Given two intersecting lines,

1. **Problem statement:** Find the measure of angle $C$ in triangle $ABC$ with sides $AB=8$, $BC=7$, and $AC=13$. The angle to find is at vertex $C$. 2. **Formula used:** Use the L

1. **State the problem:** We need to find the measure of angle $\angle C$ in triangle $ABC$ where sides $AB=5$, $BC=10$, and $AC=11$. 2. **Formula used:** Use the Law of Cosines to

1. **Problem statement:** Find the unknown side lengths in the right triangles using the Pythagorean theorem, giving answers in surd form. 2. **Formula:** For a right triangle with

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.