📐 geometry

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

1. **State the problem:** We are asked to determine if two triangles are similar and to give reasons for their similarity. 2. **Recall the similarity criteria for triangles:**

1. **Problem statement:** Determine if 18-cm by 24-cm tiles can cover a floor measuring 6.48 m by 15.12 m without cutting tiles. 2. **Convert floor dimensions to centimeters:**

1. **State the problem:** We are given two intersecting lines forming vertical angles. One angle measures $81.7^\circ$ and the angle vertically opposite to it is labeled $h$. We ne

1. The problem asks to find the value of angle $r$ given that it forms a linear pair with an angle of $69.1^\circ$. 2. Recall that angles forming a linear pair are supplementary, m

1. **Stating the problem:** We need to find the volume of a three-dimensional stepped block shape with given dimensions. 2. **Understanding the shape:** The shape consists of two p

1. **State the problem:** Find the volume of a composite solid made of two rectangular prisms stacked along the length.

1. The problem asks which statement is true based on the diagram of parallelograms, rhombuses, squares, and rectangles. 2. From the description, squares are inside both rhombuses a

1. **State the problem:** We are given a parallelogram ABCD with angles expressed in terms of $x$: - $m\angle DAB = 85 - 2x$