📐 geometry

1. **State the problem:** We have triangle $\triangle HIJ$ with side $h = 97$ cm opposite angle $H$, angle $H = 144^\circ$, and angle $I = 24^\circ$. We need to find the length of

1. **State the problem:** We have two similar trapezoidal shapes A and B. Shape A has sides: top = 5 cm, bottom = 7 cm, height = 15 cm.

1. **Énoncé du problème** : On considère un parallélépipède rectangle ABCDA'B'C'D'. Il faut démontrer plusieurs relations vectorielles entre les points. 2. **Rappel des propriétés*

1. **State the problem:** You asked why angle $x$ is $90^\circ$ when the triangle is not right-angled.

1. **State the problem:** We have a circle with center O and a triangle ABC inscribed in it. The segment AB is the diameter of the circle.

1. **Problem:** Determine which combinations of sides are Pythagorean triples. 2. **Definition:** A Pythagorean triple consists of three positive integers $a$, $b$, and $c$ such th

1. **Problem statement:** Dr. Acula jogs around a cemetery forming a polygon with the following path: 3.5 km east, 5 km northeast, 5 km northwest, 5 km southwest, and 3.5 km south,

1. **Problem statement:** A surveyor wants to find the distance $d$ across a lake. The given measurements form a right triangle with legs 90 ft and $(75 + d)$ ft, and the hypotenus

1. **State the problem:** We have two congruent triangles, \(\triangle ABC\) and \(\triangle XYZ\), with corresponding parts marked. We need to identify the corresponding congruent

1. The problem asks to classify each figure as a line, ray, or line segment and show how to write it. 2. Definitions:

1. **State the problem:** We need to find the sine of angle $F$ in the first right triangle $FHG$. 2. **Analyze the given information:** The second triangle $JKI$ is a right triang

1. **State the problem:** We need to find the area of land covered by an irrigation arm that acts as the radius of a circular irrigation system with radius $r = 390$ ft. 2. **Formu

1. The problem asks to identify the types of angles \(\angle MTN\) and \(\angle NTQ\) based on their appearance in the graphs. 2. Recall the definitions of angle types:

1. 問題の説明： 右の図で、四角形ABCDにおいて、線分AB、PQ、DCが平行です。

1. **State the problem:** Find the equation of the line passing through point A(1, 2) and the centre of the circle, given that the line $3y - x = 5$ is tangent to the circle at poi

1. **Problem statement:** A circle passes through the points $(2, 3)$ and $(-1, 6)$, and its centre lies on the line $2x + 5y = -1$. We need to find: (i) the coordinates of the cen

1. **Problem statement:** Given a net of a cube with labeled edges, determine which edge joins with edge $X$ when the net is folded into a cube. 2. **Understanding the net:** The n

1. **Stating the problem:** We have a triangle ABC with sides BC = 10 ft, AB = 11 ft, and CA = 17 ft. We want to analyze or solve for properties of this triangle. 2. **Check if the

1. **State the problem:** We have a right triangle with vertices A, B, and C, where \(\angle C = 90^\circ\). The lengths of sides are \(AB = 9\) units and \(AC = 7\) units. We need

1. **Stating the problem:** We have a triangular pyramid with vertices A, B, C, and D. Given angles are \(\angle D = 39^\circ\), \(\angle A = 44^\circ\), and \(\angle BAC = 126^\ci

1. **Stating the problem:** We have a tree and a stick casting shadows that meet at point A. The stick has height 3 m (segment BE) and shadow length 5 m (segment AB). The tree's sh