📐 geometry

1. The problem is to solve for the second triangle, which typically means finding unknown sides or angles given some information. 2. The most common formulas used in triangle probl

1. The problem is to identify which shapes are rotations of shape X. 2. Shape X is an L-shape formed by two squares in a horizontal line with one extra square below the left square

1. The problem asks to identify which shapes are rotations of Shape X. 2. Shape X is a rectangle of dimensions 4 units by 1 unit, oriented horizontally.

1. **Problem statement:** Given a circle with center O, lines BD and CE intersect at O. We know:

1. **State the problem:** We are given a circle with center O and points A, B, C on the circumference. The tangent DB is extended to T, with angle TBA = 62°. We need to find the va

1. The problem asks to identify the type of quadrilateral for the center shape KLMN, given that all angles at K, L, M, and N are right angles. 2. Recall the definitions:

1. **State the problem:** We are given a right triangle formed by points B, A, and C, where BA is the hypotenuse with length 35, one leg (from B to the foot of the perpendicular on

1. **Problem Statement:** (i) Show that any two angle bisectors of a triangle meet in a point.

1. **Problem Statement:** Prove that if two right triangles have one leg and the hypotenuse respectively equal, then the triangles are congruent. This is known as the Right-Angle-S

1. **Problem statement:** Calculate the surface areas of the cuboid, the triangular prism, and then the total surface area of the toy house formed by attaching the prism on top of

1. **Problem statement:** We need to find the size of angle $ABC$ in the quadrilateral $ABCD$ where $AB=17$ mm, $BC=14$ mm, $CD=25$ mm, $DA=19$ mm, and angle $D=53^\circ$. 2. **App

1. **State the problem:** We have a larger rectangle made up of 14 small rectangles. Each small rectangle has a height of 12 mm. We need to find the area of the larger rectangle. 2

1. **Stating the problem:** We are given two triangles with right angles and some side lengths. We need to find the missing sides or verify the given sides using the Pythagorean th

1. **Problem statement:** We are given a quadrilateral WUTV with diagonals WT and UV, where WT is parallel to UV.

1. **State the problem:** We are given the diameter $D=11.6$ m of a sphere and need to find its volume $V$. 2. **Formula:** The volume of a sphere is given by

1. **State the problem:** We need to find the unknown angle $x$ in three different triangles given the other angles. 2. **Recall the rule:** The sum of the interior angles in any t

1. **Stating the problem:** We have a square-based pyramid with base vertices C, D, E, F and apex B. Point A is the intersection of the diagonals CF and DE of the base.

1. The problem asks to write a congruency statement for triangles \(\triangle JKL\) and \(\triangle QRS\) given that \(\triangle JKL \cong \triangle QRS\). 2. A congruency statemen

1. The problem states that we have a triangle with three interior angles: $20^\circ$, $3x$, and $x$. We need to write an equation for the sum of these angles and then find the valu

1. **State the problem:** We are given a rectangle with height 5 cm and width $r - 4$ cm. The area of the rectangle is 10 cm$^2$. We need to find the value of $r$. 2. **Formula for

1. **State the problem:** We have a triangle with one angle measuring 36° and two sides labeled as 2t and 4t. We need to find the value of $t$. 2. **Understand the problem:** Since