📐 geometry

1. **Problem Statement:** We are given triangle MTR with point T above segment MR. The triangle has two equal sides: MT = TR, and angles at T are 35° and 25° on either side. Points

1. **State the problem:** We need to find the measure of angle $\angle MNT$ in the given triangle configuration. 2. **Analyze the diagram and given information:**

1. **State the problem:** Given that $m\angle BHG = 100^\circ$, find $m\angle CED$ in the given quadrilateral with intersecting diagonals and marked congruent segments and right an

1. **State the problem:** Find the angle between the x-axis and the line joining the points $(3, -1)$ and $(4, -2)$. 2. **Formula used:** The angle $\theta$ between the x-axis and

1. **Problem:** A cube has an edge length of 2 cm. Find the total surface area of the cube. 2. **Formula:** The total surface area $S$ of a cube with edge length $a$ is given by:

1. **State the problem:** We have a circular garden with radius $1.5$ m and a regular hexagonal patio inscribed inside it. We need to find the area covered by grass, which is the a

1. **Problem statement:** We have a square with a triangle inside it formed by a diagonal. The triangle has angles 45° and 70°, and we need to find the unknown angle $x$ inside the

1. **State the problem:** We need to show that the points (4, 4), (3, 5), and (-1, -1) form a right-angled triangle without using the Pythagoras theorem. 2. **Approach:** Instead o

1. **State the problem:** We need to show that the points (4, 4), (3, 5), and (-1, -1) form a right-angled triangle without using the Pythagoras theorem. 2. **Recall the concept:**

1. **Problem statement:** We are given that \(\triangle PQR \cong \triangle TSR\). We know some angles and side lengths, and we need to find the length of \(\overline{PR}\) and the

1. **State the problem:** We need to show that the points (4, 4), (3, 5), and (-1, -1) form a right-angled triangle without using the Pythagoras theorem. 2. **Approach:** Instead o

1. **State the problem:** Prove that triangles $\triangle ABC$ and $\triangle ADC$ are congruent given that $m\angle BAC = m\angle DAC = 51^\circ$, $AB = AD = 4$, and they share si

1. **Problem Statement:** We are given two triangles ABC and BCD sharing side BC. Sides AB and CD are both 5.5 units, sides BD and AC are both 3.4 units. Angles ABC and ACB are 38°

1. **State the problem:** We need to find the coordinates of the image of triangle \(\triangle CDE\) after a 180° counterclockwise rotation about the origin. The original points ar

1. **Problem statement:** Find a point on the x-axis that is equidistant from the points $(7,6)$ and $(3,4)$. 2. **Key idea:** A point on the x-axis has coordinates $(x,0)$. We wan

1. **Problem statement:** Given a circle with points $P$, $V$, and $N$ on the circumference and a point $Q$ outside the circle, we know the lengths $PV = 8$ cm, $NQ = 23$ cm, and w

1. **Problem Statement:** Find the area of a triangular fish pen with sides 16 m, 18 m, and 25 m using Heron's formula. 2. **Formula:** Heron's formula for the area $A$ of a triang

1. Given: □EASY is a parallelogram. 2. In a parallelogram, opposite sides are congruent and opposite angles are congruent.

1. The problem asks to determine the truth value of statements about parallelograms. 2. Statement 1: "A quadrilateral is a parallelogram if both pairs of opposite sides are congrue

1. The problem asks: Which quadrilateral has four right angles and 4 congruent sides? 2. Important definitions:

1. Given that □EASY is a parallelogram, opposite sides are congruent. Therefore, $AS \cong EY$. 2. Opposite angles in a parallelogram are congruent. So, $\angle A \cong \angle S$.