📐 geometry

1. The problem involves analyzing two trapezoids, Figure A and Figure B, positioned on a coordinate grid. 2. We want to find the area of each trapezoid using the trapezoid area for

1. The problem asks which postulate proves that triangles △ABE and △CDE are congruent based on the given information. 2. The postulates for triangle congruence include:

1. **Problem Statement:** We are given two triangles, \(\triangle JKL\) and \(\triangle OMN\), with the information that side \(JK \cong OM\), angle \(K \cong M\), and a third pair

1. The problem asks which postulate proves that the triangles are congruent given an isosceles triangle ABC with CD perpendicular to AB, and AC = BC. 2. Important information: AC =

1. **State the problem:** We have two congruent triangles \(\triangle RWS \cong \triangle TUV\). We need to find the values of \(x\) and \(y\) given the angles and sides. 2. **Iden

1. **Problem Statement:** Determine which congruency statement is correct among the given options for triangles $\triangle ABC$ and $\triangle DEC$. 2. **Given Information:**

1. **Problem Statement:** Given a circle with center O and arcs AB = 60°, BC = 40°, and DE = 30°, find the measures of angles labeled 1 through 11 based on the given arcs and chord

1. The problem involves understanding the properties of a right triangle with a hypotenuse of length $\sqrt{3}$.\n\n2. In a right triangle, the hypotenuse is the longest side, oppo

1. The problem is to apply the Pythagorean theorem to triangle ABC, which is a right triangle. 2. The Pythagorean theorem states that in a right triangle, the square of the hypoten

1. The problem states that there isn't a right-angled triangle between points A, B, and C. 2. To verify if a triangle is right-angled, we use the Pythagorean theorem: $$a^2 + b^2 =

1. **State the problem:** We need to find the equation of a circle given its center $C$ and radius $r$. 2. **Recall the formula for a circle's equation:** The standard form is $$ (

1. **State the problem:** Lucas and Neal walk on two circular paths given by the equations:

1. **Énoncé du problème :** On travaille dans le plan complexe avec les points A(-1,1), B(2,-2), C(2,2), D(2,-1) et le cercle \(\mathscr{C}\) de centre C et rayon 2.

1. **Stating the problem:** We have a circle with center $O$ and a chord $AB$ of length 16 cm.

1. **Problem Statement:** We are given a triangle ABC with point D on segment BC such that AB = AD and BD = DC. The angle at vertex C is 40°. We need to find the value of angle \(\

1. **State the problem:** We want to analyze the function $$T = \frac{\sqrt{2000 - 80x + x^2}}{2}$$ and related expressions, which represent distances involving a lifeguard, a poin

1. **State the problem:** We need to find the value of $x$ in a house-shaped figure composed of a rectangle and an isosceles triangle on top. The rectangle has a diagonal of length

1. **Problem 1: Triangular face and pyramid heights** Since the figure is not fully described, we assume a triangular face of a pyramid with base and height given or implied.

1. The first pair shows two L-shaped figures where one is smaller and inside the other. Since the size changes and one is inside the other, this is not a simple translation, reflec

1. **Problem statement:** Given \(\angle AYR = 30^\circ\) and \(\angle AYP = 45^\circ\), find \(\angle RYP\). 2. **Understanding the problem:** Points \(A, Y, R, P\) lie on a circl

1. **Problem Statement:** Given \(\angle MBR = 15^\circ\) and \(\angle MBP = 45^\circ\), find \(\angle RBP\). 2. **Understanding the problem:** Points \(B, P, J, R, M\) lie on a ci