📐 geometry

1. The problem asks: Which of the following is a solid figure? 2. The options are:

1. **Problem statement:** Given a right triangle with points A, B, C, and D such that triangle ABC is right-angled at A, with sides AB = 3, BC = 5, BD = \sqrt{11}, and DC = 6. 2. *

1. Énonçons le problème : Trouver le point R qui divise le segment CD selon le rapport 3:1. 2. Données :

1. **State the problem:** Determine if the triangles are congruent and by which method (SSS, SAS, AAS, ASA) or if none applies. 2. **Given:**

1. **Stating the problem:** Determine the area of the polygon in part (a) with sides 5.3 cm, 3 cm, 3.5 cm, 6.1 cm, and 2.5 cm.

1. The problem asks to write a true biconditional statement about angle bisectors. 2. A biconditional statement uses "if and only if" to show equivalence between two conditions.

1. **State the problem:** We have a right triangle with angles 45°, 30°, and 90°, and sides labeled with $p$ opposite the 45° angle and $10\sqrt{3}$ adjacent to the 30° angle. We n

1. **State the problem:** We have a right triangle with a hypotenuse of length 6 and two angles of 60° and 45°. We need to find the length of side $x$, which is opposite the 45° an

1. The problem is to find the length of the hypotenuse $c$ of a right triangle with legs measuring 6 cm and 8 cm. 2. We use the Pythagorean theorem, which states that in a right tr

1. **Problem statement:** Find the tangent ratios for angles $\angle Y$ and $\angle Z$ in a right triangle with vertices $X$, $Y$, and $Z$, where $X$ is the right angle. 2. **Given

1. **State the problem:** We have a right triangle NML with a right angle at M. Angle N is 46° and side NL (opposite angle M) is 4.1 units. We need to find side NM (adjacent to ang

1. **Problem statement:** We are given a right triangle PQR with right angle at P, and segment PQ is parallel to segment TS. We need to find which ratio is equivalent to $\tan Q$.

1. The problem states that triangles $\triangle QRP$ and $\triangle STP$ are similar, denoted as $\triangle QRP \sim \triangle STP$. 2. Similar triangles have corresponding angles

1. **Énoncé du problème :** Calculer les longueurs $AB$, $BC$ et $ME$ dans le triangle $ABC$ avec les données : $BE=5$, $EA=10$, $BM=2$, $MC=4$, $AF=16$, $AC=24$.

1. **Problem statement:** Given a triangle with sides JK = 7 cm, IJ = 8 cm, and IK = 5 cm, construct the perpendicular bisector of segment [K] and find point E, the reflection of K

1. **State the problem:** We need to find the circumference $C$ of a circle with diameter $d = 10$ m. 2. **Formula:** The circumference of a circle is given by $$C = \pi d = 2\pi r

1. The problem asks to find the circumference of a circle with radius $r = 8$ inches. 2. The formula for the circumference $C$ of a circle is:

1. **Problem statement:** Find the angles marked with letters given that CAB is always a straight line.

1. **State the problem:** Find the volume of a cylinder and the area of a circle with radius $r=21$ cm. 2. **Formulas:**

1. **State the problem:** Find the volume of a cube with side length 12 cm. 2. **Formula:** The volume $V$ of a cube with side length $s$ is given by:

1. **State the problem:** We are given two triangles, \(\triangle TUV\) and \(\triangle WXY\), with some angles known. We need to determine if these triangles are similar. 2. **Lis