📐 geometry

1. **Problem Statement:** Find the angles $\angle LADE$, $\angle LABE$, and $\angle LBED$ in the given quadrilateral with vertices $O$, $D$, $B$, $C$, and point $E$ on segment $OC$

1. **State the problem:** We have a trapezium with parallel sides of length $x - 4$ and $x + 5$, height $2x$, and area given as 351 cm². 2. **Recall the area formula for a trapeziu

1. Énonçons le problème : On a un point $E(4, 10)$ situé sur la droite d'équation $y = -0,5x + 12$. Nous devons trouver le point $F$ sur la même droite, tel que la distance entre $

1. **State the problem:** Identify which pair of angles among the given options are consecutive interior angles. 2. **Recall the definition:** Consecutive interior angles are pairs

1. The problem asks to show that the total area of the shaded regions inside the rectangle is $18x - 30$ cm². 2. First, find the area of the rectangle. Its width is $x + 6$ and hei

1. **State the problem:** Identify which pairs of angles are consecutive interior angles given the lines and transversal with labeled points. 2. **Recall the definition:** Consecut

1. **Stating the problem:** We are asked to identify which pairs of angles are supplementary from the pairs: \(\angle GHJ \text{ and } \angle DEH\), \(\angle GHE \text{ and } \angl

1. **State the problem:** Identify which pairs of angles are supplementary, meaning their measures add up to $$180^\circ$$. 2. **Recall that supplementary angles** are two angles w

1. **State the problem:** We are given two rectangles, KLMN and its dilation K'L'M'N'. We need to find the scale factor of the dilation. 2. **Understand dilation:** A dilation with

1. Problem 1: Two chords intersect inside the circle where one chord is split into lengths 6 and 3 and the other chord is split into lengths 4 and x. 2. By the intersecting chords

1. The problem states that pentagon JKLMN is similar to pentagon VWXYZ. 2. Similar pentagons have corresponding angles equal.

1. **State the problem:** We are given two similar triangles PQR and DEF with corresponding sides. We need to find which ratio correctly describes the relationship between their co

1. We are given that triangle △PQR is similar to triangle △XYZ. 2. From the problem, the sides of △PQR are PQ = 5, QR = 6, and PR = 10.

1. **State the problem:** We have a right-angled triangle with the vertical side length $x - 2$ cm and the horizontal side length $x + 4$ cm. 2. **Known information:** The area of

1. **State the problem:** Determine if rectangle EFGH is a dilation of rectangle ABCD with the center of dilation at the origin (0,0). 2. **List vertices and side lengths:**

1. **State the problem:** We are given two sectors of circles with given radii and central angles. We need to find the perimeter and area of the shaded regions for each sector, tak

1. The problem is to understand how to make a map in a Cartesian rectangular plane. 2. A Cartesian plane consists of two perpendicular number lines: the horizontal x-axis and the v

1. **State the problem:** Calculate the surface area of a prism shaped like a house. 2. **Identify the prism parts:** It consists of a rectangular prism (base) and a triangular pri

1. The problem asks to draw a triangle related to a bow drawing, which typically involves a triangle to represent forces or geometrical shapes. 2. Since the user requests to "draw

1. You asked to draw a triangle, but no specific details such as side lengths, angles, or coordinates were provided. 2. To represent a triangle mathematically, we need at least som

1. **State the problem:** Calculate the surface area of a right prism with a trapezoidal roof. 2. **Identify dimensions:**