📐 geometry

1. **Problem statement:** We have an isosceles triangle with two equal sides of length 24 cm each and a base of 14 cm. We need to find the length $x$, which is the height drawn fro

1. **Problem:** Determine if a triangle with sides 8 cm, 15 cm, and 17 cm is right-angled. 2. **Formula:** Use the Pythagorean theorem which states that in a right-angled triangle,

1. **Problem Statement:** Let's learn about spiral similarity, a transformation in geometry that combines rotation and dilation (scaling) about a point.

1. **Problem statement:** We have a circle with center $O$ and a tangent line $TAB$ touching the circle at point $A$. Given angles $CDE = 110^\circ$, $ACD = 65^\circ$, and $AEC = 6

1. **Problem statement:** Given an equilateral triangle $ABC$ with $AB=BC=CA$, and points $E$, $M$, $B$, $C$ such that $\triangle EBA \sim \triangle MCB$ with $\angle EBA=\angle AC

1. **State the problem:** We need to find a scaled copy of the original rectangle. 2. **Label the original rectangle:** Let the length be $L$ and the width be $W$.

1. **State the problem:** We need to find the area of a circle with diameter $18$ in, using $\pi=3.14$. 2. **Formula for area of a circle:**

1. **State the problem:** We need to find the area of a right triangle with legs of length $24$ m and $16$ m. 2. **Formula for the area of a triangle:**

1. **State the problem:** We need to determine which statements are always true for a rhombus. 2. **Recall properties of a rhombus:**

1. **State the problem:** We need to determine which statements are always true for a parallelogram. 2. **Recall properties of a parallelogram:**

1. **Problem Statement:** Identify which statements are always true for a kite. 2. **Definition and Properties of a Kite:**

1. **Problem:** Determine which statements are always true for a square. 2. **Recall properties of a square:**

1. **State the problem:** We need to determine which statements are always true for a trapezium. 2. **Recall the definition and properties of a trapezium:**

1. **State the problem:** Identify which statements are always true for a kite. 2. **Recall properties of a kite:**

1. The problem is to graph a circle. 2. The standard formula for a circle with center at $ (h, k) $ and radius $ r $ is:

1. **Problem Statement:** We need to find the measure of angle $B$ in triangle $ABC$ where:

1. **State the problem:** We need to find the measure of angle $A$ in triangle $ABC$ where angle $B = 37^\circ$, side $BC = 8$ ft, and side $AC = 5$ ft. 2. **Identify known element

1. **State the problem:** We need to find the length of side $BC$ in triangle $ABC$ where $AB=10$ km, $\angle A=64^\circ$, and $\angle B=74^\circ$. 2. **Find the missing angle:** T

1. **State the problem:** We need to find the length of side $BC$ in triangle $ABC$ where $AB=10$ km, $AC=20$ km, and angle $A=68^\circ$. 2. **Formula used:** We use the Law of Cos

1. **State the problem:** We need to find the measure of angle $C$ in a triangle with sides $a=55$, $b=50$, and $c=90$. 2. **Formula used:** The Law of Cosines states:

1. **State the problem:** We need to find the measure of angle $C$ in a triangle with sides $a=9$, $b=8$, and $c=5$. 2. **Recall the Law of Cosines formula:**