Tenth Grade (Grade 10) Geometry and Measurement Questions

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Grade 10 Quadrilaterals CCSS: HSG-CO.C.11

What is the missing reason in step 4 of the following proof?

Given: Quadrilateral [math]ABCD[/math] where [math]bar{AD}[/math] || [math]bar{BC}[/math] and [math]bar{AD} ~= bar{BC}[/math]
Prove: [math]bar{AB} " || " bar{CD}[/math]

Parallelogram ABCD v3

[math] \ \ \ \ \ \ \ \ \ \ \ \ " Statement " \ \ \ \ \ \ \ \ \ \ \ \ [/math]	[math] " Reason "[/math]
[math]1. bar{AD} " \|\| " bar{BC} [/math]	[math]1. "Given"[/math]
[math]2. ang CBD ~= ang ADB [/math]	[math]2. "Alternate interior angles are congruent"[/math]
[math]3. bar{BC} ~= bar{AD}[/math]	[math]3. "Given"[/math]
[math]4. bar{BD} ~= bar{BD} [/math]	[math]4. ""[/math]
[math]5. Delta ABD ~= Delta CDB [/math]	[math]5. "Side-Angle-Side Postulate"[/math]
[math]6. ang ABD ~= ang CDB [/math]	[math]6. "Corresponding angles of congruent triangles are congruent"[/math]
[math]7. bar{AB} " \|\| " bar{CD}[/math]	[math]7. "If two lines are cut by a transversal, and alternate interior"[/math] [math] \ \ \ \ \ " angles are congruent, the lines are parallel"[/math]

Reflexive Property
Diagonals of a parallelogram are congruent
Given by the diagram
Corresponding sides of congruent triangles are congruent

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.A.2

Are these two triangles similar?
Triangle ABC: [math]ang A=28°, ang B=91° [/math]
Triangle DEF: [math]ang D=28°, ang E=61° [/math]

Yes, the triangles are similar.
No, the triangles are not similar.

Grade 10 Pythagorean Theorem and Applications CCSS: HSG-SRT.C.8

The circle shown has a circumference of 47.1 in. What is the area of square ABCD which is inscribed in the circle? Round the answer to one decimal place.

Not enough information.
56.3 squared inches
112.4 squared inches
449.4 squared inches

Grade 10 Pythagorean Theorem and Applications CCSS: HSG-SRT.C.8

In the circle pictured, [math]O[/math] is the center of the circle and [math]bar{AD}[/math] is tangent to the circle. If [math]AD = 5 \ "cm"[/math] and [math]DO = 6.4 \ "cm"[/math], what is the length of the diameter of the circle, rounded to one decimal place? Hint: A line tangent to a circle is perpendicular to the radius of the circle at that point.

2.4 cm
4.0 cm
8.0 cm
16.2 cm

Grade 10 Pythagorean Theorem and Applications

Using the following measurements, find the length of the leg of the right triangle.
leg = 5
hypotenuse = 13

12
13
144

Grade 10 Pythagorean Theorem and Applications CCSS: HSG-SRT.C.8

If AC = 8 m and AB = 12 m, what is the length of [math]bar{CD}[/math], rounded to one decimal place?

2.7 m
5.3 m
6.0 m
8.0 m

Grade 10 Circles

For each part of the circle listed below, choose ALL of the properties which are true about it.

	Always intersects the center of the circle	Touches only ONE point on the circle	Can form inscribed angles
Radius
Diameter
Tangent
Chord

Grade 10 Pythagorean Theorem and Applications CCSS: HSG-SRT.C.8

Using the measurements given below, find the hypotenuse of the triangle.
Leg = 20 units
Leg = 21 units

400 units
841 units
29 units

Grade 10 Points, Lines, and Planes CCSS: HSG-CO.C.9

Choose the correct missing reason from step 3.

Given the parallel lines [math]k[/math] and [math]m[/math], and transversal [math]t[/math], prove that [math]ang 1 ~= ang 7[/math].

Parallel Lines - Skew Transversal

[math] \ \ \ \ \ \ " Statement " \ \ \ \ \ \ [/math]	[math] " Reason "[/math]
[math]1. k " \|\| " m[/math]	[math]1. "Given"[/math]
[math]2. ang 1 ~= ang 5[/math]	[math]2. "Corresponding angles are congruent"[/math]
[math]3. ang5 ~= ang 7 [/math]	[math]3. [/math]
[math]4. ang 1 ~= ang 7 [/math]	[math]4. "Substitution property of equality"[/math]