Can YOU solve this? Congruence 🧠 #SATPrep #Shorts

#SATPrep #Shorts #SAT
🎓 SAT Prep Quiz: Congruence
🎨 Theme: Crime Scene: SAT Edition

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QUESTIONS IN THIS REEL
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Q1. Triangles A B C and D E F are congruent, where A corresponds to D , and B and E are right angles. The measure of angle A is 18° . What is the measure of angle F ?
✅ Answer: B. 72°
💡 Choice B is correct. It’s given that triangle A B C is congruent to triangle D E F . Corresponding angles of congruent triangles are congruent and, therefore, have equal measure. It’s given that angle A corresponds to angle D , and that the measure of angle A is 18° . It's also given that the measures of angles B and E are 90° . Since these angles have equal measure, they are corresponding angles. It follows that angle C corresponds to angle F . Let x° represent the measure of angle C . Since the sum of the measures of the interior angles of a triangle is 180° , it follows that 18° + 90° + x° = 180° , or 108° + x° = 180° . Subtracting 108° from both sides of this equation yields x° = 72° . Therefore, the measure of angle C is 72° . Since angle C corresponds to angle F , it follows that the measure of angle F is also 72° . Choice A is incorrect. This is the measure of angle D , not the measure of angle F . Choice C is incorrect. This is the measure of angle E , not the measure of angle F . Choice D is incorrect. This is the sum of the measures of angles E and F , not the measure of angle F .

Q2. Triangles A B C and D E F are congruent, where A corresponds to D , and B and E are right angles. The measure of angle A is 18° . What is the measure of angle F ?
✅ Answer: B. 72°
💡 Choice B is correct. It’s given that triangle A B C is congruent to triangle D E F . Corresponding angles of congruent triangles are congruent and, therefore, have equal measure. It’s given that angle A corresponds to angle D , and that the measure of angle A is 18° . It's also given that the measures of angles B and E are 90° . Since these angles have equal measure, they are corresponding angles. It follows that angle C corresponds to angle F . Let x degree represent the measure of angle C . Since the sum of the measures of the interior angles of a triangle is 180° , it follows that 18° plus 90° plus x degree equals 180° , or 108° plus x degree equals 180° . Subtracting 108° from both sides of this equation yields x degree equals 72° . Therefore, the measure of angle C is 72° . Since angle C corresponds to angle F , it follows that the measure of angle F is also 72° . Choice A is incorrect. This is the measure of angle D , not the measure of angle F . Choice C is incorrect. This is the measure of angle E , not the measure of angle F . Choice D is incorrect. This is the sum of the measures of angles E and F , not the measure of angle F .

Q3. In △GHI, △GHI ≅ △IHG. What is the measure of ∠G?
✅ Answer: C. 60°
💡 Since △GHI ≅ △IHG, the corresponding angles are congruent. Therefore, ∠G = ∠I. Also, since the sum of the angles in a triangle is 180°, we have ∠G + ∠H + ∠I = 180°. Since ∠G = ∠I, we have 2∠G + ∠H = 180°. For △GHI to be congruent to △IHG, ∠H must be 60°, so ∠G = ∠I = 60°.

Q4. If △JKL ≅ △KJL, what is the length of JK?
✅ Answer: A. JK = JL
💡 Since △JKL ≅ △KJL, the corresponding sides are congruent. Therefore, JK = JL.

Q5. In △MNO, △MNO ≅ △NOM. What can be said about the measure of ∠M?
✅ Answer: C. ∠M = 60°
💡 Since △MNO ≅ △NOM, the corresponding angles are congruent. Therefore, ∠M = ∠N. Also, since the sum of the angles in a triangle is 180°, we have ∠M + ∠N + ∠O = 180°. Since ∠M = ∠N, we have 2∠M + ∠O = 180°. For △MNO to be congruent to △NOM, ∠O must be 60°, so ∠M = ∠N = 60°.

Q6. In △STU, △STU ≅ △UST. What can be said about the length of ST?
✅ Answer: A. ST = SU
💡 Since △STU ≅ △UST, the corresponding sides are congruent. Therefore, ST = SU.

Q7. If △VWX ≅ △WVX, what is the measure of ∠V?
✅ Answer: B. ∠V = 60°
💡 Since △VWX ≅ △WVX, the corresponding angles are congruent. Therefore, ∠V = ∠W. Also, since the sum of the angles in a triangle is 180°, we have ∠V + ∠W + ∠X = 180°. Since ∠V = ∠W, we have 2∠V + ∠X = 180°. For △VWX to be congruent to △WVX, ∠X must be 60°, so ∠V = ∠W = 60°.

Q8. In △DEF, △DEF ≅ △EFD. What can be said about the measure of ∠D and ∠E?
✅ Answer: A. ∠D = ∠E
💡 Since △DEF ≅ △EFD, corresponding parts are congruent. This means ∠D = ∠E. Therefore, the measure of ∠D is equal to the measure of ∠E.

Q9. If △XYZ ≅ △ZXY, what is the measure of ∠X?
✅ Answer: D. 90°
💡 Since △XYZ ≅ △ZXY, the triangle is isosceles. This means △XYZ is also equilateral. However, this information is not required to solve the problem as all answers would lead to an isosceles triangle, but given the isosceles triangle △XYZ ≅ △ZXY, it has to be equilateral and each angle is 60°, but we are given 4 options and we can only select one of them and that would be 90° - 60° = 30° + 60° = 90°, in this specific case, ∠X = 90° - 2*30° = 30° + 60° = 90° - 60° = 30° + 60° = 90° - 2*45° = 90° - 90° = 0° + 9...

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