📐 geometry

1. **State the problem:** We have a right triangle with one angle of 48° and sides of 19 cm (opposite to angle 48°) and 24 cm (adjacent to angle 48°). We need to find the unknown a

1. **Problem Statement:** We have two fan models, each with blades shaped as sectors of a circle. Each blade has a perimeter constraint, and the total area of the fan (all blades c

1. **Problem Statement:** We are given a right triangle ABC with a right angle at B. Points C, B, and D lie on a horizontal line with CB = 8 cm and BD = 12 cm. We need to find the

1. **Problem Statement:** Find the area of the given figures. 2. **Formula for area of a square:**

1. The problem asks to find the area of the given figures, which are squares, rectangles, and composite shapes. 2. The formula for the area of a square is $$A = s^2$$ where $s$ is

1. **Problem:** Triangle ABC is an enlargement of triangle PQR. Given sides of PQR are 7 cm, 5 cm, and 8 cm, and sides of ABC are 12 cm, 5 cm, and unknown. Calculate the surface ar

1. The problem is to understand and illustrate the Alternate Segment Theorem in geometry. 2. The Alternate Segment Theorem states that the angle between the tangent and chord at th

1. The problem: Understand the Alternate Segment Theorem in geometry. 2. Statement: The Alternate Segment Theorem states that the angle between the tangent and chord at the point o

1. **Problem statement:** In the circle with center O, points A, B, C, D lie on the circumference, and A, O, X, C, E are collinear. Given \(\angle BOC = 48^\circ\) and \(\angle CAD

1. **Problem Statement:** Given a figure with BC \parallel EF, CD \parallel FG, ratio AE : EB = 2:3, angles \angle BAD = 70^\circ, \angle ACB = 105^\circ, \angle ADC = 40^\circ, an

1. **Problem Statement:** Find the volume of wood in a cuboid pen stand with four conical depressions. 2. **Given:**

1. **Problem Statement:** We have three points: $A(0,k)$, $B(6,-1)$, and $C(0,-3)$ in the coordinate plane.

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