Géométrie
Triangles, cercles, géométrie analytique et démonstrations.
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simplify using the properties of exponents. circle your final answer. 1…
1. $m^9$ 2. $m^{14}$ 3. $-3x^2y^{11}$ 4. $\frac{5}{3}a^{10}b^4$ 5. $-125x^{15}y^{12}$ 6. $x^6$ 7. $27a^{11}b^{24}$ 8. $-32x^{10}$ 9. $c^3d^3$ 10. $\frac{5}{4}m^{12}$ 11. $10a^{13}…
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¿que triángulo es? hallc la medida del tercer ángul
# Explicación: ## Paso 1: Suma ángulos de triángulo La suma de ángulos en un triángulo es $180^\circ$. ## Paso 2: Ángulos iguales en isósceles En triángulo isósceles, $\angle A = …
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the sides of a triangle are 58, 33, and 85. use the pythagorean theorem…
The triangle is obtuse because the square of the largest side is greater than the sum of the squares of the other two sides.
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the sides of a triangle are 8, 10, and 6. use the pythagorean theorem t…
The triangle is right because the square of the largest side equals the sum of the squares of the other two sides.
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complete the proof. given: ( ac = 35 ) and ( ab + bc = ac ) prove: ( x …
| Statements | Reasons | |------------|---------| | $AC = 35$ | Given | | $AB + BC = AC$ | Given | | $(2x - 1) + (x + 6) = 35$ | Substitution Property of Equality | | $3x + 5 = 35…
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9. name all the angles that are congruent to angle 1.
∠3, ∠5, ∠7
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8. find the value of x that makes m || n. explain your reasoning. x = _…
\(x = 15.2\)
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7. what must be true about lines n and m in order for angles 1 and 2 to…
Lines $n$ and $m$ must be parallel.
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6. find the value of x. x = (5x - 1)° (x + 79)°
$20$
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5. find the values of x and y. x = y =
$x = 16$ $y = 100$
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4. draw a picture that shows what vertical angles are. what is always t…
Vertical angles are always **congruent (equal in measure)**. (Example diagram description: Two straight lines intersecting at a point, forming four angles. Label the pair of oppos…
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3. show an example of the substitution property of equality.
Example: 1. Let $x = 5$ and $y = x$ 2. Substitute $x$ with 5 in the expression $2y + 3$: $2(5) + 3 = 13$ This shows since $x=y$, we can substitute $x$ for $y$ (or vice versa) in a…
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proof 33) write a two - column proof. given ( mangle1 = 115^{circ} ) an…
| STATEMENTS | REASONS | |------------|---------| | 1. $m\angle1 = 115^\circ$, $m\angle2 = 65^\circ$ | 1. Given | | 2. $m\angle1 + m\angle2 = m\angle1 + m\angle2$ | 2. Reflexive P…
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with mathematics the diagram of the control bar of the kite shows the a…
The 108° angles are congruent corresponding angles formed by the control bar (transversal) with lines \(m\) and \(n\). By the Corresponding Angles Postulate, this proves \(n \para…
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in the diagram, are \\(\\overleftrightarrow{ac}\\) and \\(\\overleftrig…
Yes, $\overleftrightarrow{AC}$ and $\overleftrightarrow{DF}$ are parallel. The supplementary angle of $143^\circ$ is $37^\circ$, which matches the given $37^\circ$ angle, forming …
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8) there is a horizontal straight line with two arrows (left and right)…
\(x = 32\)
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5) m n 150° (3x - 15)°
\(x = 15\)
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find the value of x that makes m || n. 4) 5)
\(x = 15\)
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29. match each point on the number line to one number in the table belo…
To solve this, we first simplify each square root: - $\boldsymbol{\sqrt{17}} \approx 4.123$ (between 4 and 5) - $\boldsymbol{\sqrt{0.81}} = 0.9$ (close to 1, left of 1) - $\boldsy…
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ideo for extra example 3 – proving theorems about parallel lines rite a…
| STATEMENTS | REASONS | |------------|---------| | 1. $\angle 1$ is supplementary to $\angle 2$. | 1. Given | | 2. $m\angle 1 + m\angle 2 = 180^\circ$ | 2. Definition of suppleme…
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visit www.bigideasmathvideos.com to watch the flipped video instruction…
$x = 13$
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proving a theorem a2) use the reason bank to prove the consecutive inte…
| STATEMENTS | REASONS | |------------|---------| | 1. $p \parallel q$, and $t$ as the transversal | 1. Given | | 2. $\angle1 \cong \angle3$ | 2. Alternate Interior Angles Theorem…
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problem solving 17) a group of campers tie up their food between two pa…
$104^\circ$
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9. 65° 5 (11x - 17)°
$x = 12$
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find the value of x. show your steps. (see example 27)
$x = 26$
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evaluate independent practice lesson 10.2 homework complete problems a2…
## Problem 3: $m\angle1 = 63^\circ$ (Same-Side Interior Angles Theorem) $m\angle2 = 117^\circ$ (Corresponding Angles Theorem) ## Problem 5: $m\angle1 = 122^\circ$ (Corresponding A…
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visit www.bigideasmathvideos.com to watch the flipped video instruction…
$m\angle 2 = 37^\circ$. $\angle 1$ and $\angle 2$ are alternate interior angles formed by a transversal cutting two parallel horizontal lines, so they are congruent.
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the flipped video instruction for the \try this\ problem(s) below. sing…
$y = 9$
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try this video for extra example 2 and 3 - using pr 2) find the value o…
$30$
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visit www.bigideasmathvideos.com to watch the flipped video instruction…
1. $\boldsymbol{\angle 2 = 75^\circ}$; Vertical Angles Congruence Theorem 2. $\boldsymbol{\angle 6 = 75^\circ}$; Corresponding Angles Postulate 3. $\boldsymbol{\angle 7 = 75^\circ…
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example 1 - identifying angles given ( mangle 1 = 105^circ ), find ( ma…
- $m\angle 1 = 75^\circ$ (given) - $m\angle 2 = 105^\circ$ (Linear Pair Postulate with $\angle 1$) - $m\angle 3 = 105^\circ$ (Vertical Angles Congruence Theorem with $\angle 2$) -…
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name: directions: now graph and label quadrilateral to prove that it is…
1. **Graph**: Quadrilateral $SMRT$ is formed by plotting and connecting $S(1, 2)$, $M(2, -1)$, $R(8, 1)$, $T(7, 4)$ in order on the coordinate grid. 2. **Proof**: Since opposite s…
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problems 1–3: draw a cylinder. 1. label the radius 3 units and the heig…
1. (Drawing: A cylinder with radius labeled 3 units and height labeled 10 units) 2. $9\pi$ square units 3. $90\pi$ cubic units 4. 2.5 inches 5. Container A's base has a larger are…
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1. the volume of a cone is 36π cubic units. what is the volume of a cyl…
1. $108\pi$ cubic units 2. $\frac{175\pi}{3}$ cubic units 3. Cylinder: $62.8$ cubic centimeters; Cone: $20.9$ cubic centimeters 4. | Radius (m) | Volume (cu. m) | |------------|--…
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area of triangle =? a b p is 6 cm, and there is a figure with rectangle…
\(18\mathrm{cm}^2\)
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1. draw a cylinder with a diameter of 6 centimeters and a volume of 36π…
- The cylinder has a radius of 3 cm and height of 4 cm. - For the drawing: Sketch a cylinder, mark the radius of the circular base as 3 cm, and the vertical height as 4 cm.
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26. which operation is used first to solve for $f$ in $gf + h = i$? a. …
26. c. Subtraction 27. c. $2w + 2(2w + 3) = 30$
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9. a rectangle has a length of 3 times its width. if the perimeter is 4…
b. \( 2w + 2(3w) = 48 \)
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what is the area of this figure? write your answer using decimals, if n…
$223.5$ square meters
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in circle c, diameter \\(\\overline{fd}\\) is perpendicular to chord \\…
$\angle DCB$
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$\\overleftrightarrow{ab}$ is tangent to circle $d$. what is $m\\angle …
$56.5^\circ$
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which of the following graphs corresponds to the following set? $(-inft…
The first graph (with open circle at -4 and arrow to the left)
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on the venn diagram, which region(s) represent the union of set a and s…
I, II, and III
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consider the following sets. u = {ordered pairs on a coordinate plane} …
\( (0, 0) \)
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use the graph at the right. find the vertices of the image of qrtw for …
\( (-1, 2) \)
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which diagram represents the following sets? p = {x | x is an integer d…
The left - most diagram (the first one among the three)
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based on the venn diagram, which of the following statements is correct…
C. Set D is a subset of set A.
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consider the following sets: p = {x | x is a parallelogram} c = {x | x …
R. \( R = \{x \mid x \text{ is a rectangle}\} \)
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which of the following are true about x? check all that apply. \\(\\squ…
- \( x \in B \) - \( x otin C \) - \( x \in A \cup B \) - \( x \in A \cup C \) - \( x \in A \cap B \)
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which venn diagram represents the set relationship $a \\subset b$?
The fourth Venn diagram (the one where the circle labeled A is entirely inside the circle labeled B, and B has a region outside A) represents \( A \subset B \).
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21. solve for ( x ) and graph the solution on the number line below. if…
The simplified single inequality is $x > 4$. The number line has an open circle at 4 and is shaded to the right of 4.
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consider the following sets: u = {points on the coordinate plane} a = {…
\( m = 2 \)
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in $\\triangle feg$, point $h$ is between points $e$ and $f$, point $j$…
\( FJ = 18 \)
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what is the value of x? enter your answer, as a decimal, in the box. x =
\(3.5\)
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finding angles find the value of the labelled angles. (a) (b) 5.9 cm (c…
### Part (a) # Explanation: ## Step 1: Identify the sides relative to angle \( x \) In the right - triangle, the opposite side to \( x \) is \( 6\space\text{cm} \) and the adjacen…
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view submission \\overline{bc} is parallel to \\overline{de}. what is a…
34
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the universal set in this diagram is the set of integers from 1 to 15. …
- Only A (left square): None (or if the diagram's left square is for A only, maybe the problem expects 1? Wait, re - checking factors of 15: 1,3,5,15. Odd integers: 1,3,5,7,9,11,1…
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there is a coordinate grid (a grid - like coordinate system with x - ax…
The intersection point is \((-4,1)\)
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40 if ( x ) is less than 5, ( 2x ) will be less than 10. 41 graph an in…
On the provided number line: 1. Place an open circle at the mark labeled 5. 2. Draw a solid line from this open circle to the left, covering all values from 5 towards -10.
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the measure of ∠bgh can be calculated. the measure of ∠bgh is 45° becau…
The measure of $\angle BGH$ is 45° because $\angle BGH$ and $\angle ZGB$ are **a linear pair**
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the measure of ∠bgh can be calculated. the measure of ∠bgh is 45° becau…
a linear pair angles
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reflect the figure over the line $y = -1$. plot all of the points of th…
To solve the reflection of a figure over the line \( y = -1 \), we follow these steps for each vertex of the original figure: ### Step 1: Identify the original vertices First, we …
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40 aubrey has $20 to spend on party supplies. she buys balloons for $16…
1. The completed statement: If $x$ is **less than** 4, $x + 16$ will be less than 20. 2. The solution to the inequality is $x \leq 4$. For the graph: - Place a filled circle at 4 …
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the perimeter of the trapezoid - shaped window frame is 23.59 feet. wri…
Equation: $3.65 + 5.62 + 5.62 + x = 23.59$ $x = 8.7$
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reflect the figure over the line $y = -1$. plot all of the points of th…
The reflected points are \((-8,0)\), \((-6,5)\), \((-4,7)\), \((-3,7)\) (You need to plot these points on the coordinate plane. The process involves taking each original point, ap…
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find the value of x . x = 8 ×
\(x = 66\)
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find the measures of $\\angle x$ and $\\angle y$. $m\\angle x= \\boldsy…
$m\angle X = \boxed{92}^\circ$, $m\angle Y = \boxed{92}^\circ$
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9 practice 9 (from unit 1, lesson 20) here is triangle abc $\\angle bde…
Lines \( m \) and \( l \) are parallel because \( \angle BDE \cong \angle BAC \) (given), and these are corresponding angles formed by transversal \( BA \). By the Corresponding A…
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which fraction is represented on the number line below? 0 2 \\(\frac{7}…
\(\frac{8}{5}\) (the option corresponding to \(\frac{8}{5}\))
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practice 6 (from unit 4, lesson 12) a regular hexagon and a regular oct…
A. The perimeter of the hexagon is less than the perimeter of the octagon, and each perimeter is less than the circumference of the circle.
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practice 3 name 2 figures for which a circle can be a cross - section.
1. Sphere 2. Cylinder
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what fraction of the whole is shaded?
\(\frac{7}{8}\)
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given \\(\\overline{cd} \\cong \\overline{ae}\\), prove \\(\\triangle a…
To fill the flowchart: 1. First Statement Box: $\boldsymbol{\overline{AE} \cong \overline{CD}}$ (Type: $XY \cong WZ$, where $XY = AE$, $WZ = CD$), Reason: Given. 2. Second Stateme…
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given \\(\\overline{ab} \\cong \\overline{cb}\\), prove \\(\\triangle a…
To prove $\triangle ABE \cong \triangle CBD$: 1. **Statement 1**: $\overline{AB} \cong \overline{CB}$; **Reason**: Given. 2. **Statement 2**: $\angle A \cong \angle C$; **Reason**…
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question 8: consider this figure. find the area, in square feet, of the…
30
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factor the trinomial. explain what tool or technique you used. 21. ( x^…
21. $(x-5)(x+1)$ 22. $(t+5)(t-4)$ 23. $(z+8)(z-9)$ 24. $(m+3)(m-9)$ 25. $(a+7)(a-3)$ 26. $(v+2)(v-6)$ 27. $(c+4)(c-11)$ 28. $(r+8)(r-2)$ 29. $(f+3)(f-2)$ 30. $(j+5)(j-11)$ 31. $(y…
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se the figure below to find the following: a. sin a b. cos a c. tan a d…
a. \( \sin A = \boldsymbol{\frac{5}{13}} \) b. \( \cos A = \boldsymbol{\frac{12}{13}} \) c. \( \tan A = \boldsymbol{\frac{5}{12}} \) d. \( \csc A = \boldsymbol{\frac{13}{5}} \) e.…
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which pairs of figures are congruent? which pairs are similar? congruen…
First Pair (Circles): Congruent: Yes (if same size) / No? Wait, maybe in the grid, they are same. Let's assume: Congruent: Yes; Similar: Yes Second Pair (L - Shapes): Congruent: N…
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which pairs of figures are congruent? which pairs are similar? (image o…
s: - First Pair: Congruent? Yes; Similar? Yes - Second Pair: Congruent? No; Similar? No - Third Pair: Congruent? No; Similar? No - Fourth Pair: Congruent? No; Similar? No
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deltamath.com given ( ab cong cb ), prove ( \triangle abe cong \triangl…
To prove \( \triangle ABE \cong \triangle CBD \): 1. Statement: \( AB \cong CB \), Reason: Given. 2. Statement: \( \angle A \cong \angle C \), Reason: Given (diagram marks). 3. St…
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given \\(\\overline{ab} \\cong \\overline{cb}\\), prove \\(\\triangle a…
To prove $\triangle ABE \cong \triangle CBD$: 1. **Statement**: $\overline{AB} \cong \overline{CB}$ **Type of Statement**: $\overline{XY} \cong \overline{WZ}$ (with $XY = AB$, $WZ…
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given \\(\\overline{ab} \\cong \\overline{cb}\\), prove \\(\\triangle a…
To fill the flowchart: 1. First statement (angle): $\angle A \cong \angle C$ (Reason: Given, from diagram marks) 2. Second statement (side): $\overline{AB} \cong \overline{CB}$ (R…
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given \\(\\overline{cd} \\cong \\overline{ae}\\), prove \\(\\triangle a…
To fill the flowchart: 1. First box (statement): $\angle A \cong \angle C$ (Reason: Given by the tick marks in the diagram, indicating congruent angles) 2. Second box (statement):…
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a lawyer drives from her home, located 7 miles east and 21 miles north …
26
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based on the given diagram, prove $\\triangle abe \\cong \\triangle cbd…
To prove \( \triangle ABE \cong \triangle CBD \): 1. Statement: \( \boldsymbol{\overline{BE} \cong \overline{BD}} \), Reason: Given (marked congruent segments). 2. Statement: \( \…
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determine whether the graph is the graph of a function. select one: a. …
A. Yes
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jeff wants to propose a neighborhood crosswalk for greater biker and wa…
B. a proposal letter describing the need, benefits, and costs of a new crosswalk
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solve for x. x = ? ft round to the nearest hundredth
\(6.17\)
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a recycling bin is in the shape of a rectangular box. find the height o…
The height of the box is \( \boxed{7} \) ft.
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8. the sides of each square in the potholder measure 1 inch. what are t…
There are 180 seconds in 3 minutes. ### Question 8 (assuming the potholder is a 5x5 grid - like shape with some squares, but we can count the area by counting the number of 1 - in…
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you just plotted two non-solutions to our equation, (4, 6) and (4, 3). …
The points (4, 6) and (4, 3) do not lie on line n.
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k about her sister’s husband? given. write the letter of the correct ch…
s: 13. E 14. H 15. F 16. N 17. I 18. W 19. C 20. R 21. L 22. T 23. T 24. B (Note: Some steps may have had initial confusion, but corrected by re-evaluating the right triangle side…
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the two triangles below are similar. complete the similarity statement.…
$\triangle HIJ \sim \triangle RPQ$ ### Part 2: Finding the Ratio of Side Lengths
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révision éclair pour décrire la position d’une figure dans un plan cart…
### Part 1: Matching Coordinates to Points (Sub - question 1) #### a) For \((20,15)\) - Looking at the second grid (with the \(x\) - axis from \(0\) to \(30\) and \(y\) - axis fro…
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the two polygons below are similar. complete the similarity statement. …
\(RQPS\) ### Part 2: Finding the Side Length Ratio
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given: $ef \\parallel gh$ and $ab \\parallel cd$. prove: $\\angle ijl$ …
\( \angle IJL \) and \( \angle JLK \) are supplementary (proven as above).
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the two polygons below are similar. complete the similarity statement. …
\(GJIH\) ### Part 2: Finding the Ratio of Side Lengths
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the two polygons below are similar. complete the similarity statement. …
\( GDEF \) ### Part 2: Finding the Ratio of Side Lengths
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what is the value of x? (there is a diagram of two intersecting lines w…
$13$
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find x, then find the measurement of both angles.
$x = 30$ Measure of both angles: $114^\circ$