📐 geometry

1. **Problem Statement:** Prove that in triangle $ABC$, where side $BC$ is extended to $D$, and $BE$ and $CE$ are bisectors of angles $\angle ABC$ and $\angle ACD$ respectively, th

1. The problem states that Maria has an original triangle with side lengths 6 inches, 8 inches, and 10 inches. 2. The teacher suggests drawing a similar triangle with a scale facto

1. The problem asks for the additional information needed to prove triangles congruent given a specific reason (ASA, SAS, or SSS) and one pair of congruent parts. 2. For each case,

1. **Problem statement:** Given a vertical pole AB with point A at the top and B at the bottom on the ground, point C is 2 m to the right of B on the horizontal line. Point D lies

1. **State the problem:** We have a circle with center O and points A, B, C, D on the circumference.

1. The problem is to find the area of Unit 1, which typically refers to the area of a unit square or unit shape with side length 1. 2. The formula for the area of a square is given

1. **Énoncé du problème :** Dans l'exercice 1, on a un trapèze rectangle ABCD en A avec :

1. (a) Problem: Triangle ABC is an enlargement of triangle PQR. Given sides of PQR: 7 cm, 8 cm, 5 cm; and side QR of ABC is 12 cm. Find the surface area of triangle ABC. Step 1: Id

1. Problem: Prove that two triangles are congruent using the Side-Angle-Side (SAS) criterion. Formula: If two sides and the included angle of one triangle are equal to two sides an

1. The problem asks for the coordinates of the midpoint of the line segment OE, where O is at (0,0) and E is at (14,22). 2. The formula for the midpoint $M$ of a segment with endpo

1. **State the problem:** We need to find the coordinates of point M, which is the midpoint of the line segment CD. 2. **Formula for midpoint:** The midpoint M of a segment with en

1. **Problem statement:** We are given the center of a circle at point $C(2,1)$ and a point on the circle $P(8,9)$. We need to find:

1. **Problem Statement:** Given two overlapping circles with points A, B on the larger circle and points D, O on the smaller circle, and given angles 90° at D, 42°, 30°, and 120°,

1. **Problem statement:** Given a cone with radius $r = x$ and height $h = 4x$, prove that its volume is $\frac{4}{3}\pi x^3$. 2. **Formula for volume of a cone:**

1. **State the problem:** We need to find the volume of water in the trough when the water depth is three quarters of the height of the trough. 2. **Given dimensions:** Length = 1.

1. **Stating the problem:** We are given a right triangle with sides BC = 5 inches, CD = 5 inches, and AD = 13 inches. We need to find the length of side AB in centimeters, knowing

1. **Problem Statement:** Calculate the total surface area of a frustum of a right pyramid with rectangular base ABCD where $AB=32$ cm, $BC=24$ cm. The top face EFGH is parallel to

1. **State the problem:** Calculate the total surface area of the frustum formed by cutting a right pyramid ABCD with a plane EXOH parallel to the base. 2. **Given data:**

1. **Énoncé du problème 23** : Trace un triangle ABC. Place D et E les milieux respectifs de [AB] et [BC]. Place un point F sur [AC], tel que la distance d(F, E) = d(F, E) (probabl

1. The problem asks to find the length of a cube given its volume is 3375 cm³. 2. The formula for the volume of a cube is $$V = s^3$$ where $s$ is the length of a side.

1. **Problem statement:** We have an equilateral triangle $\triangle ABC$ and a square $DEFG$ inscribed inside it such that $D$ lies on $AB$, $E$ on $BC$, and $F$ on $AC$. Lines $A