📐 geometry

1. **State the problem:** We have a trapezium ABCD with angles at vertices A, B, and D given as $y$, $100^\circ$, and $84^\circ$ respectively. We need to find the value of $y$. 2.

1. **Problem Statement:** We have a square ABCD and its dilated image A'B'C'D' centered at the origin. We need to find the scale factor of the dilation.

1. **State the problem:** We have quadrilateral ABCD with vertices A(3,5), B(5,7), C(8,2), and D(4,-1). It is dilated from the origin to quadrilateral A'B'C'D' with vertices A'(12,

1. **State the problem:** We have triangle $\triangle ABC$ with vertices $A(-2,10)$, $B(4,8)$, and $C(2,4)$. We want to find the coordinates of $A'$, $B'$, and $C'$ after a dilatio

1. **Problem Statement:** We have triangle ABC with vertices A(-2, 10), B(4, 8), and C(2, 4). We need to find the coordinates of A', B', and C' after a dilation with scale factor 3

1. Problem 4.1: In \(\triangle DEF\), \(\angle E = 90^\circ\), \(DE = 15\) m, and \(DF = 17\) m. Find the length of \(EF\). 2. Use the Pythagorean theorem for right triangles: $$DF

1. **Problem Statement:** We have a cube whose side length increases by 10%. We need to find:

1. Let's start by stating the problem: We want to understand what area means in mathematics and how to calculate it. 2. Area is the measure of the amount of space inside a two-dime

1. **Problem Statement:** Calculate the area of the irregular polygon with given side lengths 6 ft, 3 ft, 8 ft, 9 ft, 6 ft, 13 ft, 6 ft, and 8 ft. 2. **Approach:** To find the area

1. **State the problem:** Find the area of the irregular polygon shaped like an arrow using the given side lengths. 2. **Approach:** The polygon can be divided into three rectangle

1. **Problem Statement:** Find the area of the irregular polygon with given side lengths: 15 mm (left vertical), 9 mm (bottom horizontal), 6 mm (right vertical), and smaller segmen

1. **State the problem:** Find the area of the irregular polygon composed of rectangles and triangles with given side lengths. 2. **Analyze the figure:** The polygon can be divided

1. **State the problem:** We need to find the area of a compound figure composed of rectangles and a triangle with given side lengths. 2. **Break down the figure:** The figure can

1. The problem asks to identify which pairs of triangles are congruent by ASA (Angle-Side-Angle). 2. ASA congruence means two triangles are congruent if two angles and the included

1. The problem asks what additional information is needed to prove that triangle $\triangle ABC$ is congruent to triangle $\triangle DEF$ by the ASA (Angle-Side-Angle) criterion. 2

1. The problem asks which theorem is NOT valid to prove that two triangles are congruent. 2. The common triangle congruence theorems are:

1. **State the problem:** We need to determine which triangle congruence theorem proves that triangle $\triangle ABC$ is congruent to triangle $\triangle DEF$ given that side $BC =

1. **Problem Statement:** We have two right triangles, \(\triangle ABC\) and \(\triangle DEF\). \(\triangle ABC\) has legs \(y\) (vertical) and \(x\) (horizontal), and hypotenuse 1

1. **State the problem:** We need to determine which given information can be used to prove that triangle ABC is congruent to triangle DEF. 2. **Given information:**

1. **Problem Statement:** Determine which theorem can be used to show that triangle ABC is congruent to triangle DEF given that side AB equals side DE, side AC equals side DF, and

1. **Problem Statement:** We have an isosceles triangle RST with RS = ST. Point M(2,0) is the midpoint of RT, and \(\angle RMO = 45^\circ\). Point S has coordinates \((k,5)\). We n