Take This Important Geometry Trivia Test!

The missing information is Division. In step 4, the equation is divided by 2 on both sides to isolate the variable x. This step is necessary to solve for x and find its value.

The given statement is justified by the property of substitution. According to this property, if two angles have a sum of 90 degrees and one of the angles is known to be 20 degrees, then the other angle can be found by substituting the known value into the equation. In this case, m∠A + m∠B = 90, and m∠B = 20, so by substituting 20 for m∠B in the equation, we get m∠A + 20 = 90. Therefore, the answer is substitution.

The given statement "If ∠A ≅ ∠B and ∠B ≅ ∠C, then ∠A ≅ ∠C" can be justified by the transitive property of congruence. According to this property, if two angles are congruent to a third angle, then they are congruent to each other. In this case, ∠A ≅ ∠B and ∠B ≅ ∠C, so by the transitive property, ∠A ≅ ∠C. The term "substitution" is not applicable in this context and does not justify the statement.

State the definition, property, postulate, or theorem that justifies each statement.

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The measure of angle EFD is 20 degrees. This can be determined by using the property that angles on a straight line add up to 180 degrees. Since angle BFC is given as 70 degrees, the sum of angles BFC and EFD must be 180 degrees. Therefore, angle EFD is 180 - 70 = 110 degrees. However, since angle EFD is an exterior angle to triangle BFC, it is equal to the sum of the opposite interior angles. Since angle BFC is 70 degrees, the other interior angle, angle EFB, must be 110 - 70 = 40 degrees. Finally, since angle EFD is an alternate interior angle to angle EFB, they must be congruent, so angle EFD is also 40 degrees.

The Segment Addition Postulate states that if point B is between points A and C on a line, then the sum of the lengths AB and BC is equal to the length of AC. In this case, AB and BC are added together to give the length of AC, which justifies the statement AB + BC = AC.

If ∠ABC ≅ ∠EFG and m∠ABC = 72, then the measure of ∠EFG is also 72 degrees. Since ∠GFH is vertical to ∠EFG, it will also have a measure of 72 degrees. Therefore, the correct answer is 18.

The property that justifies the statement "If x = 2 and x + y = 3, then 2 + y = 3" is Substitution. Substitution is the property that allows us to replace a variable with its value in an equation or expression. In this case, we are given that x = 2 and x + y = 3. By substituting the value of x, which is 2, into the second equation, we get 2 + y = 3. Therefore, the correct answer is Substitution.

The property that justifies the statement m∠A = m∠A is the reflexive property. The reflexive property states that any element is equal to itself. In this case, it means that the measure of angle A is equal to itself, which is always true.

Since ∠ABC ≅ ∠DBJ and m∠ABJ = 28, we can conclude that m∠ABC = m∠DBJ = 28. Since the sum of the angles in a triangle is 180 degrees, we can calculate m∠JBC by subtracting the known angles from 180: 180 - 90 - 28 = 62. However, we need to find m∠JBC, not m∠BCJ. Therefore, we subtract 62 from 90 to get the final answer of 28.

The statement "If two planes intersect, then their intersection is a point" is false. When two planes intersect, their intersection can be a point, a line, or even the entire plane. Therefore, it is incorrect to say that their intersection is always a point, sometimes a point, or cannot be determined. The correct answer is "Never" because the statement is never true.

The definition of congruent segments states that if two segments have the same length, then they are congruent. In this case, if segment PR is congruent to segment QT, it means that they have the same length. Therefore, PR must be equal to QT.

The property that justifies the statement "If  ≅ , then   ≅ " is the Symmetric property. This property states that if two segments are congruent, then their order can be reversed. In other words, if segment AB is congruent to segment CD, then segment CD is also congruent to segment AB.

To find x, we can set the two given angle measures equal to each other and solve for x. So, we have 5x - 10 = 3x + 20. By subtracting 3x from both sides and adding 10 to both sides, we get 2x = 30. Dividing both sides by 2, we find that x = 15. Therefore, the answer is 15. However, this contradicts the given correct answer of 21.25. Without further information or clarification, it is difficult to determine the correct value of x.

The point Z is between the other two points X and Y because the given information states that XZ = 2, which is smaller than XY = 6 and YZ = 4. Therefore, Z must be the point between X and Y.

The Complementary Angles Theorem states that if two angles are complementary to the same angle or congruent angles, then they are congruent to each other. In this case, we are given that angle X and angle Z are congruent and angle X and angle Y are complementary, as well as angle Z and angle Q are complementary. Therefore, by applying the Complementary Angles Theorem, we can conclude that angle Y and angle Q are congruent.