📐 geometry

1. **State the problem:** Identify which pairs of angles are supplementary. Supplementary angles are two angles whose measures add up to $$180^\circ$$. 2. **Recall the rule:** When

1. State the problem: We need to prove that $\triangle YOG$ is similar to $\triangle FOX$ given that $FX \parallel YG$.

1. The problem is to plot the circle given by the equation $$(x-1)^2+(y-1)^2=9.$$ 2. This is the equation of a circle in standard form: $$(x-h)^2+(y-k)^2=r^2,$$ where $(h,k)$ is th

1. **State the problem:** We need to plot the circle given by the equation $$(x-1)^2+(y-1)^2=9$$. 2. **Formula and explanation:** The general form of a circle's equation is $$(x-h)

1. **State the problem:** We need to find the total surface area of a triangular prism given its net with dimensions 3.3 cm, 4.4 cm, 5.5 cm, and 7.1 cm. 2. **Identify the shapes in

1. **State the problem:** We need to find the image of rhombus $EFGH$ after two transformations: a reflection across the line $y = -1$ and then a translation 14 units left and 1 un

1. **State the problem:** We need to find the image of triangle $\triangle XYZ$ with vertices $X(-5, 12)$, $Y(-11, 9)$, and $Z(-8, 6)$ after a glide reflection consisting of a tran

1. **State the problem:** We have a rectangle with length $14$ cm and breadth $8$ cm, and a semicircle attached along the breadth side. The diameter of the semicircle is $8$ cm.

1. **State the problem:** We need to find the point where the pole should be placed to balance the triangular bird bath. This point is the centroid of the triangle formed by vertic

1. **Problem Statement:** We need to find and graph the orthocenter of $\triangle ABC$. The orthocenter is the point where the three altitudes of a triangle intersect. 2. **Recall:

1. **Problem Statement:** We are asked to graph the image of a figure after applying reflections across the x-axis or y-axis as specified in six different problems.

1. **Problem Statement:** We need to graph the image of a figure after applying reflections across the x-axis and y-axis as specified. 2. **Reflection Rules:**

1. **Problem Statement:** We are asked to graph the images of various figures after reflecting them across either the $y$-axis or the $x$-axis.

1. **State the problem:** We need to find the perimeter of $\triangle TUV$ given the side lengths $TU = 63$ and $VU = 74.8$. We must find the length of side $TV$ to complete the pe

1. **State the problem:** We need to find the perimeter of $\triangle DEF$, where two sides are given as $28$ and $22.4$, and the third side $x$ is unknown. The angles are $57^\cir

1. **State the problem:** We need to find the area of a triangle given its vertices. 2. **Formula:** The area of a triangle with vertices at coordinates $(x_1,y_1)$, $(x_2,y_2)$, a

1. **State the problem:** We need to find the volume of a triangular prism with a triangular base of base length $5$ cm and height $4$ cm, and prism length $10$ cm. 2. **Formula fo

1. **State the problem:** We need to design a network of speaker stations to cover the barangays Malanday, Tumana, and Nangka, each with given centers and flood warning radii. Each

1. **Problem Statement:** In circle $\odot O$, chord $AB$ and segment $OC$ intersect at point $M$. Given that $OM = MC$ and $AM = 1.5$, $BM = 4$, find the length of $OC$. 2. **Rele

1. **State the problem:** We need to find the area of a right triangle with legs of lengths $5$ cm and $12$ cm, and a hypotenuse of $13$ cm. 2. **Formula:** The area $A$ of a right

1. The problem asks to fill in the blanks related to parts of a circle. 2. The distance around the circle is called the **circumference**.