📐 geometry

1. **State the problem:** We are given a pentagon with interior angles labeled as $4x$, $(5x + 3)$, $(2x + 1)$, $(4x + 14)$, and $4x$ degrees. We need to solve for $x$. 2. **Recall

1. **Problem Statement:** Given an isosceles triangle with vertex $O$ and base points $E$ and $V$, where the two sides meeting at $O$ are congruent and the segment $EV$ is split in

1. The problem is to determine if the two triangles shown are congruent and if yes, state the theorem that proves their congruence. 2. The common theorems to prove triangle congrue

1. The problem asks to identify the triangle congruence criteria shown in the diagram with two right triangles sharing a hypotenuse and a leg. 2. The key congruence criteria for ri

1. **State the problem:** Prove that triangles $\triangle LMN$ and $\triangle PON$ are congruent. 2. **Given:**

1. **State the problem:** Given that $E$ is the midpoint of segments $GN$ and $WQ$, prove that $WN \cong GQ$. 2. **Understand the given information:** Since $E$ is the midpoint of

1. **Problem statement:** Given quadrilateral ABCD with AB = 9, BC = 10, AB ∥ DC, angle B = 63°, and a perpendicular height from C to AD with foot length 4, find the perimeter of A

1. **State the problem:** We have a quadrilateral ABCD with AB parallel to DC, AB = 9, BC = 10, AD = 4, and angle B = 63°.

1. **State the problem:** Find the area of parallelogram ABCD given the base and height. 2. **Formula:** The area $A$ of a parallelogram is given by:

1. **State the problem:** Find the area of rectangle GHIJ given the side lengths. 2. **Recall the formula for the area of a rectangle:**

1. **State the problem:** Find the scale factor given the corresponding coordinates of points before and after scaling. 2. **Formula:** The scale factor $k$ is found by dividing th

1. The problem asks whether the dilation of Figure A to Figure B is an enlargement or a reduction. 2. Dilation is a transformation that changes the size of a figure by a scale fact

1. **Problem:** Translate rectangle QRST with vertices Q(-6, -1), R(-3, 1), S(1, -5), and T(-2, -7) by the rule $(x, y) \to (x + 5, y + 7)$. 2. **Formula:** To translate a point $(

1. **Problem statement:** We need to find the length of the red line segment in a complex polygon composed of triangles with given side lengths 12, 4, 1, 15, and 1 (red segment). 2

1. **State the problem:** We need to find the tangent of angle $W$ in a right triangle with sides opposite and adjacent to $W$ given as 12 and 37 respectively. 2. **Recall the form

1. **Problem statement:** Find the cosine of angle $X$ in a right triangle $XVW$ where the right angle is at vertex $V$. The sides are $XV=36$, $XW=85$, and $VW=77$. 2. **Recall th

1. **State the problem:** Find the cosine of angle $F$ in right triangle $FDE$ where $\angle D$ is the right angle. 2. **Recall the cosine definition:** For an angle in a right tri

1. **State the problem:** We need to find the cosine of angle $T$ in right triangle $TUV$ where $TU=20$, $UV=48$, and hypotenuse $TV=52$. 2. **Recall the cosine definition:** In a

1. **State the problem:** We have a quadrilateral with two known angles: 96° and 110°, and two missing angles labeled 1 and 2. We need to find the values of angles 1 and 2. 2. **Re

1. **State the problem:** We are given the coordinates of triangle UVW and need to find the slopes and lengths of its sides, then classify the triangle.

1. **Stating the problem:** We have a circle with four inscribed angles measuring 80°, 32°, 25°, and three unknown angles labeled $a$, $b$, and $c$ opposite the known angles. We wa