📐 geometry

1. The problem asks to find the measure of the missing angle $a$. 2. We know that the two angles $a$ and 51° form a right angle, which means their sum is 90°.

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

1. **Problem Statement:** We are given an affine plane with axioms I1 to I4 and need to prove four properties about parallel lines, points on lines, total points, and provide an ex

1. **Problem Statement:** Given two chords AB and CD of a circle intersecting at point E inside the circle, prove that $|AE| \cdot |EB| = |CE| \cdot |ED|$.

1. **Problem statement:** In pentagon ABCDE, all sides are equal and angles A, B, C are equal. We need to prove all five angles are equal, making it a regular pentagon. 2. **Given:

1. **Problem Statement:** Solve the two triangles given the following data: - Triangle 1: \(\angle A = 19^\circ\), \(a = 30\) yd, \(b = 12\) yd, \(m\angle B = 69.5^\circ\), \(m\ang

1. **State the problem:** We are given a triangle with some sides and angles labeled inconsistently. We need to solve the triangle, meaning find all unknown sides and angles.

1. **Problem statement:** In pentagon ABCDE, all sides are equal and angles A, B, C are equal. We need to prove all five angles are equal, making it a regular pentagon. 2. **Given:

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