📐 geometry

1. **State the problem:** We have two triangles, \(\triangle TUV\) with vertices \(T(4,4), U(2,2), V(6,2)\) and \(\triangle T'U'V'\) with vertices \(T'(0,0), U'(-10,-10), V'(10,-10

1. Let's clarify the problem you are referring to and identify the correct answer for the translation. 2. Translation in geometry means moving every point of a figure or a space by

1. **State the problem:** We have two triangles, \(\triangle HIJ\) and \(\triangle H'I'J'\), where \(\triangle H'I'J'\) is obtained by translating \(\triangle HIJ\) and then perfor

1. **State the problem:** We need to find the translation rule and the scale factor of the dilation centered at the origin that transforms triangle ABC with vertices A(-5,1), B(-7,

1. **State the problem:** We have two triangles, $\triangle STU$ with points $S(4,3)$, $T(8,2)$, $U(7,0)$ and $\triangle S'T'U'$ with points $S'(0,0)$, $T'(8,-8)$, $U'(4,-10)$. We

1. **State the problem:** We are given two triangles, $\triangle STU$ with vertices $S(3,4)$, $T(7,2)$, $U(5,0)$ and $\triangle S'T'U'$ with vertices $S'(-2,0)$, $T'(8,-8)$, $U'(4,

1. **State the problem:** Find the area of rectangles given their length and width. 2. **Formula:** The area $A$ of a rectangle is given by

1. Problem: İki doğru AD ve EB, F noktasında kesişiyor. Verilen açı ölçüleri $\angle AFB = 45^\circ$ ve $\angle DFC = 30^\circ$. Bu bilgilerle verilen açı ölçülerinden hangisinin y

1. **State the problem:** A 25-foot ladder is placed against a vertical wall, with the foot 7 feet from the base. The top slips down 4 feet. We need to find how far the foot slides

1. **State the problem:** We have two triangles, \(\triangle ABC\) and \(\triangle DEF\), with given angles and sides. We need to: a. Use the Triangle Angle Sum Theorem to find the

1. **Problem statement:** We have a window shaped with a parabola on top and a circular arc below. The parabola's vertex is 4.75 ft above the x-axis, the window width is 10.7 ft, a

1. **Stating the problem:** We have triangle ABC with points P and Q on sides AB and AC respectively, and segment PQ parallel to BC. Point R lies on BC. We want to analyze the rela

1. **Problem statement:** Given triangle ABC, points P on AB and Q on AC such that PQ is parallel to BC. By Thales' theorem, we have \( \frac{|AP|}{|PB|} = \frac{|AQ|}{|QC|} \).

1. **State the problem:** We have trapezoid ABCD with legs BC and AD, DE perpendicular to CB, and given angles $m\angle A = 86^\circ$ and $m\angle C = 74^\circ$. We want to find th

1. If two lines intersect, then the vertical angles are always **congruent**. This is called the **Vertical Angles Theorem**.

1. **Problem Statement:** We need to construct a pentagon with exactly one right angle (90 degrees) and exactly one acute angle (less than 90 degrees). 2. **Understanding Angles in

1. **State the problem:** We are given the original vertices of a triangle and the vertices of a new triangle after a transformation. We need to determine which rule was applied to

1. **State the problem:** We need to find the volume of a cylinder with radius $r=5$ cm and height $h=10$ cm. 2. **Formula for the volume of a cylinder:**

1. **Problem Statement:** Determine if the pairs of lines in each graph are parallel, perpendicular, or neither. 2. **Key Concepts:**

1. **Problem Statement:** Find the area of the shaded region in a trapezoid with an inscribed rectangle.

1. **Problem Statement:** We have a rectangular prism with dimensions width = 4 mm, depth = 8 mm, and height = 11 mm. The top and bottom faces are shaded. We need to find: