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Home Question Bank Math Geometry Archive 2025 January 10

Geometry Questions from Jan 10,2025

Browse the Geometry Q&A Archive for Jan 10,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Esercizio 3. Trovare centro e raggio della circonferenza \( \mathscr{C}:\left\{\begin{array}{l}x^{2}+y^{2}+z^{2}-4 x+2 y-6 z=1 \\ x+2 y-2 z=0\end{array}\right. \) Esercizio 4. Siano dati il piano \( \pi: 2 x-y+2 z+1=0 \) e la retta \( r:\{x+y=1 \) Given a geometric sequence where the first term is 5 and the common ratio is 3, find the sum of the first 4 terms. pecide whether enough information is given to prove that the triangles are aruent in each case below. If there is enough information, state the aruence postulate or theorem you would use. 7.) a) SAS b) SSS c) ASA d) AAS e) HL f) Not Congruent 4.) Assume all given information to be true. \( \begin{array}{ll}\text { If a figure is a square, then it has four sides. } & \text { 4.) } \\ \text { a.) If a figure has four sides, th } \\ \text { is a square. }\end{array} \) What conclusion can you draw from the following? \( \begin{array}{ll}\text { b.) If a figure is not a triangle, } \\ \text { it is a square. }\end{array} \) c.) If a figure is a square, then not a triangle. 3.) Assume all given information to be true: \[ \begin{array}{ll}\text { If } m \angle A \text { is less than } 90^{\circ} \text {, then } \angle A \text { is an acute angle. } & \text { 3.) } \\ \text { The measure of } \angle A=75^{\circ} & \text { b.) } \angle A \text { is an acute angle. } \\ \text { W.) is a right angle. } & \text { c. is an obtuse angle. } \\ \text { What can you logically conclude? } & \text { d.) Not enough informatio }\end{array} \] a) If \( m \angle M O N=51^{\circ} \), find \( m \angle N O K \). b) If \( m \angle J O K=40^{\circ} \) and \( m \angle N O M=2 x+8 \), find the value of \( x \). c) If \( m \angle J O K=5 x^{\circ} \) and \( m \angle K O N=(17 x+26)^{\circ} \), find the value of \( x \). 4. Find the distance between points \( Q(2,4) \) and \( R(-3,9) \). Question 6 (40) Grayson is painting a picture. The picture has an area of \( \frac{5}{6} \) square yard. Which could be the dimensions of the painting? What is the midpoint of \( (3,-5) \) and \( (11,-11) ? \) Why is the perpendicularity of tangents and radii important in solving geometric problems involving circles? Special Right Triangles Decompose square or equilateral triangle Find the missing side lengths of the triangles. Show you work. NO ROUNDING.
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