📐 geometry

1. **State the problem:** Given that ABCD is a parallelogram, CE bisects \(\angle DEB\), and \(\angle ADE \cong \angle ABE\), prove that \(\triangle DEC \cong \triangle BEC\). 2. *

1. **State the problem:** Given that ABCD is a parallelogram, CE bisects \(\angle DEB\), and \(\angle ADE \cong \angle ABE\), prove that \(\triangle DEC \cong \triangle BEC\). 2. *

1. **State the problem:** We need to find the value of $t$ in a triangle where the angles are given as $32^\circ$, $t + 45^\circ$, and the bottom vertex angle is split into two par

1. **State the problem:** We have a quadrilateral SRQT with angles at vertices S, T, Q, and R. Given angles are \(\angle S = 100^\circ\) and \(\angle T = 61^\circ\). We need to fin

1. **State the problem:** We need to find the range of possible values of $x$ given a quadrilateral with one internal angle labeled as $(3x - 6)^\circ$, an adjacent angle of $24^\c

1. **Problem statement:** We have a triangle with sides 22 cm and 14 cm, and an angle of 35° opposite the 22 cm side. We need to find the angle $x$ at the bottom left corner. 2. **

1. **State the problem:** We need to find the measure of angle $\angle B$ in a right triangle with sides $AC=22$ and $BC=18$, where $\angle C$ is the right angle. 2. **Identify the

1. The problem is to plot the point D with coordinates $\left(0, -\frac{7}{2}\right)$ on a Cartesian coordinate grid. 2. The point $D(0, -\frac{7}{2})$ means the x-coordinate is 0

1. The problem is to plot the point B with coordinates $\left(\frac{5}{2}, 3\right)$ on a Cartesian plane. 2. The coordinates $\left(\frac{5}{2}, 3\right)$ mean the point is locate

1. The problem asks which solid, when cut by a plane parallel to its base, produces a rectangular cross section. 2. Important rule: A plane parallel to the base of a solid will pro

1. **State the problem:** Find the surface area of a rectangular prism with dimensions 4 cm, 5 cm, and 3 cm. 2. **Formula:** The surface area $SA$ of a rectangular prism with lengt

1. **State the problem:** Find the surface area of a rectangular prism with dimensions height $h=6$ in, width $w=4$ in, and depth $d=7$ in. 2. **Formula for surface area of a recta

1. **State the problem:** Find the surface area of a rectangular prism with dimensions 7 cm (height), 3 cm (width), and 1 cm (depth). 2. **Formula:** The surface area $S$ of a rect

1. **State the problem:** We need to find the area of a figure composed of a rectangle and two semicircles attached on the shorter sides. 2. **Identify given dimensions:** The rect

1. **State the problem:** Find the area of a composite figure made of a parallelogram and a semicircle. 2. **Identify given dimensions:**

1. **State the problem:** We need to find the area of a composite figure made of a rectangle and two semicircles attached to the shorter sides of the rectangle. 2. **Identify given

1. **Énoncé du problème :** Nous avons un carré ABCD avec deux triangles équilatéraux AEB et BCF. Il faut déterminer la nature des triangles ADE et EBF, démontrer une mesure d'angl

1. **Énoncé du problème** : Nous avons un carré ABCD orienté dans le sens direct, avec deux triangles équilatéraux AEB et BCF. Il faut déterminer la nature des triangles ADE et EBF

1. **State the problem:** We need to find the surface area (area) of a scalene triangle with base $b = 5$ cm and height $h = 9$ cm. 2. **Formula:** The area $A$ of a triangle is gi

1. The problem asks to find the surface area (SA) of a given figure. 2. From the information, the figure includes a scalene triangle with base $b=9$ cm and height $h=5$ cm.

1. **Problem statement:** Tarzan wants to find the width of the river, which corresponds to the vertical distance from point A to point B. 2. **Setup:** We have a right triangle fo