📐 geometry

1. **State the problem:** We have a triangle with three interior angles: 38°, 76°, and 6c°. We need to find the value of $c$. 2. **Recall the triangle angle sum rule:** The sum of

1. **Stating the problem:** We are asked to analyze pairs of vectors in a triangular prism: $\overrightarrow{DF}$ and $\overrightarrow{EH}$, $\overrightarrow{GI}$ and $\overrightar

1. **Problem Statement:** Identify which pairs of lines in the cube are skew lines. Skew lines are lines that are neither parallel nor intersecting and do not lie in the same plane

1. **State the problem:** Given that BD bisects \(\angle ABC\) and \(\angle ADC\), prove that \(\triangle ABD \cong \triangle CBD\). 2. **Recall the definition of angle bisector:**

1. **State the problem:** We have two similar triangles ABC and ADE. Given AB = 8 cm, AE = 12 cm, ED = 3 cm, and AC = x cm. We need to find the two possible values of $x$. 2. **Rec

1. **State the problem:** We are given two pentagons, ABCDE and A'B'C'D'E', where A'B'C'D'E' is a reflection of ABCDE. We need to determine the line of reflection. 2. **Identify co

1. **State the problem:** We have triangle ABC dilated about the origin to create triangle A'B'C'. We need to find the scale factor of the dilation. 2. **Recall the dilation formul

1. **Problem statement:** Given triangles \(\triangle ABC \sim \triangle ADE\), find: a) the scale factor from \(\triangle ABC\) to \(\triangle ADE\),

1. The problem asks to find the scale factor between triangles \(\triangle ABC\) and \(\triangle ADE\), then use it to find the perimeter of \(\triangle ABC\) and the area of \(\tr

1. **Problem statement:** Given a right triangle KLM with angles at K and L both 45°, and side KM = 20, find the length of side LM. 2. **Understanding the problem:** Since angles K

1. The problem involves a rectangle with a total length of 18 cm and two horizontal bars inside it, one with a 3 cm segment on the right and the other with a 2 cm segment on the le

1. **State the problem:** We need to find the length of the missing side $w$ in a quadrilateral where the sides and angles are given as follows: one side is 20 m, and the angles ad

1. **State the problem:** We need to find the missing angle $P$ in a triangle where one angle is $20^\circ$ and the sides adjacent to angle $P$ are 15 cm and 18 cm, with the side o

1. **State the problem:** We need to find the area of a trapezium with parallel sides of lengths 9 cm and 30 cm, and a height of 8 cm. 2. **Formula for the area of a trapezium:**

1. **State the problem:** Calculate the area of a trapezium with top base $12$ cm, bottom base $6$ cm, and height $5$ cm. 2. **Formula for the area of a trapezium:**

1. **State the problem:** We need to name two similar triangles from the given diagram and explain why they are similar. 2. **Identify the triangles:** The triangles mentioned are

1. **Stating the problem:** We have two similar triangles, $\triangle ABC \sim \triangle DBE$. Given side lengths are $AC=10$, $DE=4$, and $BE=3$. We need to find the length of $AB

1. The problem is to find the volume of a cylinder with a base radius of 50 cm and a height of 5 cm. 2. The formula for the volume $V$ of a cylinder is:

1. **State the problem:** We need to find the height $h$ at which the volleyball player hits the ball. The volleyball net is 8 feet tall, the ball lands 15 feet away from the base

1. **State the problem:** We need to find the image of triangle \(\triangle JKL\) under a dilation centered at the origin with scale factor \(\frac{1}{3}\). 2. **Recall the dilatio

1. **State the problem:** We need to find the measure of angle $\angle KML$ in quadrilateral $KJML$ where $\angle J = 108^\circ$ and $\angle MNL = 25^\circ$. 2. **Understand the se