📐 geometry

1. **Problem Statement:** We have triangle ABC with side lengths |BC| = 24 cm and |AC| = 18 cm. Point L lies on side AC such that |LC| = 6 cm. Point K is the midpoint of side AB. N

1. **State the problem:** Emily breaks a stick into 3 pieces that can form a triangle. She loses one piece and measures the other two as 6 cm and 12 cm. We need to find which total

1. **Problem statement:** Find the angles $a$, $b$, and $c$ marked in the circle with diameter $AB$ and chords $AC$, $DB$, $AD$, and $BC$ intersecting inside the circle. 2. **Given

1. The user asked to recheck polygons and polyhedrons, but no specific problem or question was provided. 2. To assist effectively, please provide a specific question or problem rel

1. The problem asks to identify pairs of angles and label polygons/polyhedrons as regular (R) or irregular (I). 2. Alternate interior angles are pairs of angles on opposite sides o

1. **State the problem:** Given quadrilateral LMNO with sides LM \cong ON and LO \cong MN, prove that LMNO is a parallelogram. 2. **Recall the Parallelogram Side Theorem:** If both

1. The problem is to find the distance between two points $A(3,2)$ and $B(4,5)$ in the coordinate plane. 2. The formula to find the distance $d$ between two points $A(x_1,y_1)$ and

1. The problem describes a QR code with three visible finder squares located at the top-left, top-right, and bottom-left corners, and a small dark logo-like shape near the center.

1. **Stating the problem:** Given that triangles $\triangle ABC$ and $\triangle ADE$ are similar ($\triangle ABC \sim \triangle ADE$), we want to understand the relationships betwe

1. The problem is to identify the image as a QR code with a centered square, three corner finder squares, and a small dinosaur-like icon in the middle. 2. This is a geometry-style

1. The problem asks to write an expression in terms of $x$ for angle $ACD$. 2. From the description, angle $ACD$ is given as $\frac{180 - x}{2}$.

1. **State the problem:** Find the area of the compound figure composed of rectangles and a semicircle with given side lengths. 2. **Identify parts of the figure:** The figure cons

1. **Problem Statement:** We have two triangles, \(\triangle ABC\) and \(\triangle DEC\), with \(AB \parallel CD\) and \(DE \parallel CA\). Given side lengths \(AB = 20\) m, \(DC =

1. The problem asks to identify which diagram shows an enlargement of triangle U with a scale factor of 3 and the centre of enlargement at the cross. 2. The formula for enlargement

1. **State the problem:** We have a large triangle on a straight line base with angles 46°, 63°, y, 140°, and x as shown. We need to find the values of $x$ and $y$. 2. **Identify k

1. **State the problem:** We need to find the size of angle $x$ in a figure with two parallel horizontal lines and two transversals forming angles $137^\circ$ and $65^\circ$ as sho

1. **Stating the problem:** We need to find the formula for the area of a circle and then calculate the area of two circles: one with radius 8 cm and another with diameter 20 cm.

1. **Stating the problem:** We need to find the total number of rectangles in the given grid-like figure with 4 vertical divisions and 3 horizontal divisions arranged in a stepped

1. Bài toán yêu cầu liệt kê các cặp góc kề bù trong Hình 3.13. 2. Định nghĩa: Hai góc kề bù là hai góc có chung một cạnh, hai cạnh còn lại nằm trên cùng một đường thẳng, tổng số đo

1. **Problem statement:** Vẽ góc xOy có số đo bằng 60°. Vẽ tia Om là tia đối của Ox.

1. **State the problem:** We are given two circles with equations $$(x - 10)^2 + (y - 5)^2 = 25$$ and $$(x - 20)^2 + (y - 10)^2 = 100$$ and asked to find the length of the line seg