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Home Question Bank Math Geometry Archive 2024 December 15

Geometry Questions from Dec 15,2024

Browse the Geometry Q&A Archive for Dec 15,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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15. In \( \triangle A B C \), if \( m \angle A \) is thirteen less than \( m \angle C \) and \( m \angle B \) is eleven less than four times \( m \angle C \), find the measure of each angle. \[ \begin{array}{l}m \angle A= \\ \\ m \angle B= \\ m \angle C=\end{array} \] 21 I triangoli \( A M B \) e \( M D C \) in figura sono isosceli rispettivamente sulle basi \( A B \) e \( C D \), e \( M \) è il punto medio del segmento \( A C \). Dimostra che \( A B \cong C D \). Circle \( O \) intersects \( \overline{A B} \) only at \( F, \overline{B C} \) only at \( G \), and \( \overline{A C} \) only at \( H \). Which equation is true? Choose the correct answer below. A. \( \mathrm{m} \angle O F B=90^{\circ} \) B. \( \angle B A O \cong \angle A B O \) C. \( A H=A C \) . \( O F=O C \) 16 Sul segmento \( A B \) traccia il punto \( C \). Considera quindi i punti \( P \) e \( Q \) sui semipiani opposti origi- nati dalla retta che contiene \( A B \) e tali che \( P \overparen{C} A \cong Q \widehat{C} B \). Dimostra che i punti \( C, P \) e Q ri- sultano allineati. Sul segmento \( A B \) traccia il punto \( C \). Considera quindi i punti \( P \) e \( Q \) sui semipiani opposti origi- nati dalla retta che contiene \( A B \) e tali che \( P \widehat{C} A \cong Q \widehat{C} B \). Dimostra che i punti \( C, P \) e Q ri- sultano allineati. I1 Traccia su una semiretta orientata quattro punti, nell'ordine, \( P, Q, R, S \), tali che \( P Q \cong R S \). Dimostra che: a. \( P R \cong Q S \); b. il punto medio del segmento \( P S \) è anche il punto medio del segmento \( Q R \). What is the sum of the interior angle measures of a polygon that has 7 sides? Sum \( =[?]^{\circ} \) Gegeven het vlak \( V:\left(\begin{array}{l}x \\ y \\ z\end{array}\right)=\left(\begin{array}{l}1 \\ 0 \\ 0\end{array}\right)+\lambda\left(\begin{array}{c}-1 \\ 1 \\ -1\end{array}\right)+\mu\left(\begin{array}{c}-5 \\ 3 \\ 2\end{array}\right) \) a. Geef een normaalvector \( \vec{n} \) van \( V \). b. Stel een vectorvoorstelling op van de loodlijn uit \( O \) op \( V \). c. Stel een vectorvoorstelling op van de loodlijn \( k \) op \( V \) die door het punt \( P(0,11,3) \) gaat. d. Bereken de coodrdinaten van het snijpunt \( S \) van \( k \) en \( V \). If a triangle is right, then it has a hypotenuse. Choose the equivalent statement. If atriangle is notaright triangle, then ithas ahypotenuse. If atriangledoes nothaveahypotenuse, then itis notaright triangle. Gegeven de lijn \( k \) met vectorvoorstelling \( \left(\begin{array}{l}x \\ y \\ z\end{array}\right)=\left(\begin{array}{c}0 \\ 3 \\ -2\end{array}\right)+\lambda\left(\begin{array}{c}1 \\ -1 \\ 2\end{array}\right) \) a. Geef een vectorvoorstelling van de lijn \( m \) door het punt \( B(0,3,7) \) die \( k \) loodrecht snijdt. b. Bereken de coobrdinaten van het snijpunt \( S \) van \( k \) en \( m \). c. Bereken de lengte van het lijnstuk \( B S \).
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