📐 geometry

1. **State the problem:** We need to find the perimeter of an L-shaped figure drawn on a 6x6 grid where each square side is 1 cm. 2. **Understand the shape:** The L-shape covers 3

1. **State the problem:** Given parallelogram ABCD with diagonals AC and BD perpendicular ($AC \perp BD$), prove that $AB \cong BC$. 2. **Recall properties:** In a parallelogram, d

1. **Problem:** Given a right-angled triangle PQR with right angle at R, hypotenuse PQ = 16 cm, and leg PR = 8 cm, find the length of QR to 2 decimal places. 2. **Formula:** Use Py

1. **State the problem:** Find the length of the radius of the circle given the chords and radii in the diagram.

1. **Stating the problem:** We have a vertical figure composed of a rectangle with length $3m\ 5cm$ connected on top to an ellipse with height $85cm$ and on the bottom to another e

1. The problem is to find the area of a shape with given side lengths 2 m, 5 m, and 4 m. 2. Since the problem does not specify the shape, we assume it is a triangle with sides 2 m,

1. **Problem statement:** Find the coordinates of point $X$ on the line segment $\overline{RS}$ such that $X$ is $\frac{1}{6}$ of the distance from $R$ to $S$. 2. **Given:**

1. **Problem statement:** Find the coordinates of point X on line segment AB such that X is \(\frac{1}{5}\) of the distance from A to B. 2. **Formula:** To find a point dividing a

1. The problem is to find the formula for the area of a parallelogram. 2. The area $A$ of a parallelogram can be calculated using the formula:

1. **State the problem:** We need to determine if the new TV screen (16 inches wide and 9 inches high) is a dilation of the old TV screen (20 inches wide and 15 inches high). 2. **

1. The problem asks for the complement of the angle $90 - x$ degrees. 2. Recall that the complement of an angle $\theta$ is $90^\circ - \theta$.

1. The problem asks for the complement of an angle measured in degrees, denoted as $a$. 2. The complement of an angle is defined as the amount by which the angle must increase to r

1. **State the problem:** Find the area of a circle with radius 9 yd using $\pi = 3.14$ without rounding the answer. 2. **Formula for area of a circle:**

1. The problem asks for the sum of the interior angle measures of a convex 18-gon, which is a polygon with 18 sides. 2. The formula to find the sum of interior angles of a polygon

1. **Problem statement:** Given a quadrilateral ABCD, decompose it into triangles by drawing segments from vertex A to all non-adjacent vertices. 2. **Decomposition:** The non-adja

1. **Problem statement:** We have three similar triangles with given angles and side lengths. We need to find the values of $w$, $x$, and $y$. 2. **Recall properties of similar tri

1. **Problem statement:** Given the rectangle PQRS with vertices P, Q, R, S, find the image points P', Q', R', S' after the transformation (x, y) \to (2x, y). 2. **Transformation f

1. **Understanding Similarity:** Similarity in geometry means two shapes have the same shape but not necessarily the same size. 2. **Key Properties of Similar Figures:** Correspond

1. **Stating the problem:** Explain the concept of "chevauchements" (overlaps) in a mathematical or geometric context. 2. **Definition:** "Chevauchements" means overlaps or interse

1. **Stating the problem:** Find the surface area of a triangular prism. 2. **What is a triangular prism?** It is a 3D shape with two triangular bases and three rectangular faces c

1. **Stating the problem:** You want to understand everything about surface area to pass your exam. 2. **What is surface area?** Surface area is the total area that the surface of