Mathematics
Grade9
Easy
Question
Write a complete proof by matching each statement with its corresponding reason.
GIVEN:
is an angle bisector of
.
PROVE: ![m angle P Q S equals fraction numerator 1 over denominator 2 end fraction m angle P Q R](data:image/png;base64,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)
Statements | Reason |
A. Definition of angle bisector | |
B. Distributive Property | |
C. Angle Addition Postulate | |
D. Given | |
E. Division Property of Equality | |
F. Definition of congruent angles | |
G. Substitution Property of Equality |
- 1 - A, 2 - B, 3 - C, 4 - D, 5 - E, 6 - F, 7 - G
- 1 - G, 2 - F, 3 - A, 4 - B, 5 - C, 6 - E, 7 - D
- 1 - D, 2 - F, 3 - A, 4 - C, 5 - G, 6 - B, 7 - E
- 1 - D, 2 - F, 3 - A, 4 - E, 5 - B, 6 - G, 7 - C
Hint:
In this question , we have to match the statement to the correct reasons. Given is (QS ) ⃗ is an angle bisector of ∠PQR. Remember the property of equality to match them.
The correct answer is: 1 - D, 2 - F, 3 - A, 4 - C, 5 - G, 6 - B, 7 - E
Here we have to match the statement to the correct reasons.
We have given (QS ) ⃗ is an angle bisector of ∠PQR.
Now,
Statements Reason
Statements
Reason
is an angle bisector of ![straight angle P Q R](data:image/png;base64,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)
A. Definition of angle bisector
![straight angle P Q S approximately equal to straight angle S Q R](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHAAAAAPCAYAAAA8lEtfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAANvpXuIwAAAsFJREFUeNrlWV2EVVEUPq5rXGP0kqSH9NLDSDIk40oyJElGIhlJxqWHjPQQmYeMZEiPPUQPGRkZRpIkMcY85EokPSTpJclIL2Mk10jcvpXvsm37Z+19OpppFh9zztln3+9ba+211z5TFPl2tNjctqH13wHmPM/WgC7xA5gHRjwOeA50+M4Lz7g6cB1Y5rhXwLF1qj+Fq1a/6dNlzvkM2JZL/i6wAgw7nu0G3hrXfcAR4BOwx7h/E3gMHABqxCjwDThozfkEOMkxDWCcSfGvLKRfyzVFv+1TsWngVg75+wHyBck/cNxvAVf49yU6wWWSgS+t67kEfuNMFsnqRSaPbQMlghfSr+Waot/n0zPATCr52UjwxKaMQNkZNwHsBN4x43y2ypUrdpaB0JqUl8PM/hFm+SMGssFnrzODF9Ov4Zqq3+dTKdOXU8g/VASvYLkYte5Jrf4IbOXSn4jMsQAMGYI7nHeHgueAZ69ZAn4Bn7lKU02jX8M1Vb/Lp1uAD8B2DfEaM1gTvIKBMsnvB9rG5izZtysyhzi537geYmZLQ3Qtkr1/21L1x7jm6O/5tM6G6A1wWkO+nki+xizv8h0J3A0joDVmaOw3Vz3Pxvh+O7CPdZWoQn+Ma45+06c9HNKSf5pIfpilKjTn98gcp9gohErkLLO7SsvRH+Oao9/2aVPTffbxnJFKfkzRGXUiJbBt1X+XnQPuVbgCc/VruKbqd/l0IVSGGzxc5pC/DVxQtOG+JmJSebaRrD5R0coro1/DNVW/y6dNX5Xq5wacS172i+ORMYPAF+A8S4rYPgqddnztmOQ7ve5rih1hFVZGv5Zriv6QTxetDyN/bCmhBHUdh9YVZrB2r1wzPhFddIzbS2Ey5icPuK0K970y+lO4avWHfNpkmV8XJl8VvvKA3SrzjW+D2n+hXzq2q8D7YnP+lyNb/2+llwSnXAuZLAAAANh0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+JiN4MjIyMDs8L21pPjxtaT5QPC9taT48bWk+UTwvbWk+PG1pPlM8L21pPjxtbz4mI3gyMjQ1OzwvbW8+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPiYjeDIyMjA7PC9taT48bWk+UzwvbWk+PG1pPlE8L21pPjxtaT5SPC9taT48L21hdGg+9+xFLQAAAABJRU5ErkJggg==)
B. Distributive Property
![m straight angle P Q S equals m straight angle S Q R](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJAAAAAPCAYAAAALdkYuAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAANvpXuIwAAAvxJREFUeNrtmV9kllEcxx95zWsmJpNdpJsuJpOR5JUuIkkyicwryYwuMuliZBczyUgXXXQxkiTJy2SSzJiZZBKTLibZTZJJNzOT1yuxviffR8dxzvP8zulpz9Pr+fFhz3nO83t/v+/5fxZF+dmpqLRSv0CbBg3HuxbYJt/BDDjhEHAeNPnNa0e9CrgJ1lnvLTjdpvr55CrVT2+TdfqcAz15JX8fbICjlncHwHvtuQOcBJ/AQa38NngOjoBdZBB8A8cMny/AOdapgmF2yv/VkvST5uqjn9kmyqbAnTySf5yQfMTkn1rKR8AY/75GEW2mRtAb47nRRjN3kn7SXH30c7XJEHhkfjwJboC94B5741dwhu+7wV0msAXGPZN/ktJ54hjGHCNmFOwDqxwxLtvkzKXsIljcocbNWz9Jrr76udpELZPXzQ9nWHkF1Lme7ufy0QtesedVGEiLYknsmaDzxDEMGmVqrV0Dezh1jqb4WAADmmBN+u0VxLktICn2PPWT5Oqrn61NdoOPttjX2IO7jXK1cXrgKE9rFNXTZ4WdJ45B93kYLGubu1U2SpJ9Bp3a8wDzUhvyiZTR9zdWBP3Scg3RL26TCjfk78AFW6BN40NJeZJVPJNXPn9ylG+w49zSRJb+5qbjXZ3fK79dGXeeIuiXlmuIfnqbxBy3fagCXMqgXA/kpWfyEp9bKT7Oc6Ppsi7uJSYyXsKKoF9ariH6mXHWXKevum1XHVAeH73nApJP8hlbM2UJWjbWb5tdAg8znoGKoJ8kV1/9bHEu2JZBdWq4YnHoW17l5VRI8i6f5jF22PFuXHg3oUbl2Yw7UBH0k+Tqq58tzpptlp/Vjpuh5Z3cwIUm7/ot3frAF3CZU7KyQxRqyqg7TVH6tNPDJE80WVve+klz9dEvKX4Vp36x+zvoqqWiT/mScA8R0xD+lmv/0Ir+XLFftdTrpzCqzg9ekI38oxNY3vr55CrVLyn+GpfZtrAhXtitULSeqLRSv4ATh7oF/hCV/+XfUf1+AR0RPDPCvo4cAAAA5XRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5tPC9taT48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+JiN4MjIyMDs8L21pPjxtaT5QPC9taT48bWk+UTwvbWk+PG1pPlM8L21pPjxtbz49PC9tbz48bWk+bTwvbWk+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPiYjeDIyMjA7PC9taT48bWk+UzwvbWk+PG1pPlE8L21pPjxtaT5SPC9taT48L21hdGg+J9vASAAAAABJRU5ErkJggg==)
C. Angle Addition Postulate
![m straight angle P Q S plus m straight angle S Q R equals m straight angle P Q R](data:image/png;base64,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)
D. Given
![m straight angle P Q S plus m straight angle P Q S equals m straight angle P Q R](data:image/png;base64,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)
E. Division Property of Equality
![2 times m straight angle P Q S equals m straight angle P Q R](data:image/png;base64,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)
F. Definition of congruent angles
![m straight angle P Q S equals 1 half m straight angle P Q R](data:image/png;base64,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)
G. Substitution Property of Equality
The match are:
1 → D
2 → F
3 → A
4 → C
5 → G
6 → B
3 → E
Therefore the correct answer is 1-D, 2- F, 3 - A, 4- C, 5 - G, 6 - B, 7-E.
In this question , we have to match the statements to the correct reasons and for that , Use the Property of Equality and match with correct reason.