📐 geometry

1. **Problem statement:** We have a right-angled triangle ABC with right angle at B. AB is parallel to ED. The areas of triangles EDC and BED are 24 cm² and 72 cm² respectively. We

1. **Problem Statement:** In triangle $\triangle DEF$, point $C$ is the centroid. Given that $HD = 30x - 6y$, find the expression for $CD$.

1. **Problem Statement:** Identify a median in triangle $\triangle GBI$ using the given figure. 2. **Definition of a Median:** A median of a triangle is a line segment joining a ve

1. **Problem Statement:** We are given triangle $PQR$ with altitudes $\overline{RS}$ and $\overline{PT}$ drawn from vertices $R$ and $P$ respectively. The measure of angle $Q$ is $

1. **Problem Statement:** We are given a right triangle $\triangle ABC$ with a right angle at $A$. Points $K$ and $Q$ lie on segments $AB$ and $AC$ respectively. Segment $BK$ is gi

1. The problem asks for the size of the reflex angle given the smaller angle is approximately 50 degrees. 2. Recall that a reflex angle is the larger angle formed by two lines, whi

1. **State the problem:** We are given a circle divided into four sectors with central angles 18°, $x$, $2x$, and 147°. We need to find the value of $x$. 2. **Formula and rule:** T

1. **State the problem:** We have a circle divided into two parts: a green sector measuring 174° and an orange sector divided into three equal smaller sectors each labeled $k$. We

1. **Problem Statement:** We are given a square on the Cartesian plane with vertices A(2,2), B(6,2), C(6,-2), and D(2,-2). We want to analyze the properties of this square, such as

1. **State the problem:** We have a right triangle with a vertical side of length $n$ and a horizontal side of length 20. We want to understand the relationship between these sides

1. **Problem Statement:** We are given different scales and lengths on maps or plans and need to find actual lengths or map lengths using the scale.

1. **Problem Statement:** We are given a scale of 1:500000 and a drawn length of 15 cm. We need to find the actual length represented by this drawn length.

1. **Stating the problem:** We are given a scale where 1 cm represents 20 m, and we need to write the scale as a ratio and find the scale factor.

1. **Problem Statement:** Find the area of the colored region in the parallelogram, given that the area of square BCEF is 64 in².

1. The problem involves analyzing nine triangular shapes arranged in a 3x3 grid, each divided into three sections with numbers at vertices and centers. 2. Each triangle's numbers l

1. **Stating the problem:** We have an isosceles triangle with two equal base angles each measuring $50^\circ$. We need to find the apex angle, which is the angle opposite the base

1. **State the problem:** We have quadrilateral ABCD with AB \cong DC and a right angle at vertex D. We need to determine which two statements must be true based on the diagram. 2.

1. **State the problem:** Prove that the opposite angles of parallelogram ABCD are congruent, specifically that $\angle B \cong \angle D$. 2. **Given:** $\overline{AB} \parallel \o

1. Let's clarify the problem: You mentioned that from 4 to 8 it is not a rectangle. We need to understand what shape or figure is being discussed and what properties define a recta

1. **State the problem:** We need to prove that a parallelogram with congruent diagonals has a right angle. 2. **Given:** Parallelogram $ABCD$ with diagonals $\overline{AC} \cong \

1. The problem asks to draw two angles: \(\angle ABC = 115^\circ\) and \(\angle XYZ = 70^\circ\) to represent Cut 1 and Cut 2 for Joe's timber cuts. 2. To draw an angle, start by d